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Stefan Banach

Born March 30, 1892(1892-03-30)
Died August 31, 1945
Citizenship Austro-Hungarian, Polish, Soviet Union[1]
Nationality Polish
Fields mathematics
Institutions Lwów (Lviv) University
Alma mater Lwów (Lviv) Polytechnic
Notable awards Memberships:
Academy of Sciences of the Ukrainian SSR,
Polish Academy of Learning

Stefan Banach [ˈstɛfan ˈbanax] (Image:Ltspkr.png listen) (Ukrainian: Степан Степанович Банах; 1892–1945) was a Polish mathematician who worked in interwar Poland and in Soviet Ukraine. Events 240 BC - 1st recorded Perihelion passage of Halley's Comet. Year 1892 ( MDCCCXCII) was a Leap year starting on Friday (link will display the full calendar of the Gregorian Calendar (or a Leap year Events 1056 - Byzantine Empress Theodora becomes ill dying suddenly a few days later without children to succeed the Throne Year 1945 ( MCMXLV) was a Common year starting on Monday (link will display the full calendar Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and History Beginnings The University was founded on January 20 1661 when the King John II Casimir of Poland issued the diploma granting the city's Alma mater is Latin for "nourishing mother" It was used in Ancient Rome as a title for the mother Goddess, and in Medieval Lviv Polytechnic National University ( Львівська політехніка Національний університет, Politechnika Lwowska Национальный The National Academy of Sciences of Ukraine (Національна академія наук України Natsional’na akademiya nauk Ukrayiny) is the highest state research The Polish Academy of Learning ( Polish: Polska Akademia Umiejętności) headquartered in Kraków, is one of two institutions in contemporary Poland having Ukrainian (in Ukrainian украї́нська мо́ва ukrayins'ka mova,) is a language of the East Slavic subgroup of the Slavic languages. A mathematician is a person whose primary area of study and research is the field of Mathematics. The Second Polish Republic or interwar Poland is the Republic of Poland between World War I and World War II. The Ukrainian Soviet Socialist Republic or the Ukrainian SSR was one of the 15 constituent republics that made up the Former Soviet Union from its A self-taught mathematics prodigy, Banach was the founder of modern functional analysis and a founder of the Lwów School of Mathematics. List of child prodigies|Fictional child prodigies A child prodigy is a one who masters one or more skills or arts at an early age For functional analysis as used in psychology see the Functional analysis (psychology article The Lwów School of Mathematics (lwowska szkoła matematyczna Львівська математична школа was a group of Mathematicians who worked between the Among his most prominent achievements was the 1932 book, Théorie des opérations linéaires (Theory of Linear Operations), the first monograph on the general theory of linear-metric space. In Mathematics a linear space can mean one of two things In Linear algebra or Mathematical analysis, a Vector space In Mathematics, a metric space is a set where a notion of Distance (called a metric) between elements of the set is defined

Notable mathematical concepts named after Banach include the Banach–Tarski paradox, Hahn–Banach theorem, Banach–Steinhaus theorem, and Banach space. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and The term "concept" is traced back to 1554–60 ( l conceptum - something conceived but what is today termed "the classical theory of concepts" is the theory of Aristotle The Banach–Tarski paradox is a Theorem in set theoretic Geometry which states that a solid ball in 3-dimensional space can be split into several In Mathematics, the Hahn–Banach theorem is a central tool in Functional analysis. In Mathematics, the uniform boundedness principle or Banach-Steinhaus theorem is one of the fundamental results in Functional analysis. In Mathematics, Banach spaces (ˈbanax named after Polish Mathematician Stefan Banach) are one of the central objects of study in Functional analysis

Contents

Life

Stefan Banach was born March 30, 1892, in Cracow, then part of Austro-Hungarian Galicia. Events 240 BC - 1st recorded Perihelion passage of Halley's Comet. Year 1892 ( MDCCCXCII) was a Leap year starting on Friday (link will display the full calendar of the Gregorian Calendar (or a Leap year Kraków, in English also spelled Krakow or Cracow (ˈkrækaʊ M-W: krăk'ou krāk'ō is one of the largest and oldest cities in Poland Galicia (Галичина ( Halychyna) Galicja is a historical region in East Central Europe, currently divided between Poland and Ukraine, Banach's parents were Stefan Greczek, a young soldier in the Austro-Hungarian Army, and Katarzyna Banach, both natives of the Podhale region. The Austro-Hungarian Army was the ground force of the Austro-Hungarian Dual Monarchy (1867 - 1918 The Podhale (literally "Mountain meadows" is Poland 's most southern region sometimes referred to as the "Polish highlands" [2]. Since Banach's father was a private and was prevented by military regulations from marrying, and the child's mother was too poor to support young Stefan, the couple decided that the child should be reared by a friend of Banach's father, the owner of a Cracow laundry. A Private is a Soldier of the lowest Military rank (equivalent to NATO Rank Grades OR-1 to OR-3 depending on the force served in NOTICE TO WOULD-BE ROMEOS ************** [2] Stefan Greczek paid for his son's education and would be the only relative whom Banach would personally know. [2]

Already as a student at Cracow's Gymnasium no. A gymnasium (pronounced with ɡ- in several languages is a type of school providing Secondary education in some parts of Europe, comparable to English grammar IV, Banach became known as a prodigy. List of child prodigies|Fictional child prodigies A child prodigy is a one who masters one or more skills or arts at an early age In 1906, aged 14, he was studying higher mathematics, and two years later he had started in on several languages, western and eastern. [3] After obtaining his matura at age 18 (1910), Banach went with his friend Witold Wiłkosz to Lemberg (Polish Lwów; now Lviv, Ukraine; then the capital of Galicia), intending to enroll in engineering at the Lwów Polytechnic. Matura (Matur Maturita Maturità Maturität матура is the word commonly used in Austria, Albania, Bosnia and Herzegovina, Bulgaria Lviv ( Ukrainian: Львів, L’viv, Lwów Lemberg Львов L'vov; see also other names) is a major city in western Galicia (Галичина ( Halychyna) Galicja is a historical region in East Central Europe, currently divided between Poland and Ukraine, Lviv Polytechnic National University ( Львівська політехніка Національний університет, Politechnika Lwowska Национальный However, as Banach had to earn money to support his studies, it was not until 1914 that he finally, at age 22, passed his half-diploma exams. [4]

When World War I broke out, Banach was excused from military service due to his left-handedness and poor vision. World War I (abbreviated WWI; also known as the First World War, the Great War, and the War to End All When the Russian Army opened its offensive toward Lwów, Banach left for Cracow, to spend the rest of the war there and in other Galician towns. He made his living tutoring at local gymnasiums and working in a bookshop. In British Australian New Zealand Italian and some Canadian universities, a tutor is often but not always a Postgraduate Student or a Lecturer A gymnasium (pronounced with ɡ- in several languages is a type of school providing Secondary education in some parts of Europe, comparable to English grammar He may have attended lectures at the Jagiellonian University, but little is known of that period in his life. For several academies alternatively called "Krakow Academy" see Education in Kraków The Jagiellonian University (Uniwersytet [5]

In 1916, in Cracow's Planty gardens, Banach encountered Professor Hugo Steinhaus, one of the most renowned mathematicians of the age. Planty is a city park in Kraków, Poland. It encircles the District of Stare Miasto ( Old Town) where the medieval city Władysław Hugo Dionizy Steinhaus ( January 14, 1887 &ndash February 25, 1972) was a Polish Mathematician and Steinhaus became fascinated with the self-taught young mathematician. The encounter resulted in a long-lasting collaboration and friendship. It was also through Steinhaus that Banach met his future wife, Łucja Braus.

Steinhaus introduced Banach to academic circles and substantially accelerated his career. After Poland regained independence, in 1920 Banach was given an assistantship at Cracow's Jagiellonian University. For several academies alternatively called "Krakow Academy" see Education in Kraków The Jagiellonian University (Uniwersytet Steinhaus' backing also allowed him to receive a doctorate without actually graduating from a university. A doctorate is an Academic degree that indicates the highest level of academic achievement The doctoral thesis, accepted by Lwów University and published in 1922,[6] included the basic ideas of functional analysis, which was soon to become an entirely new branch of mathematics. History Beginnings The University was founded on January 20 1661 when the King John II Casimir of Poland issued the diploma granting the city's For functional analysis as used in psychology see the Functional analysis (psychology article The thesis was widely discussed in academic circles and allowed him in 1922 to become a professor at the Lwów Polytechnic. Lviv Polytechnic National University ( Львівська політехніка Національний університет, Politechnika Lwowska Национальный Initially an assistant to Professor Antoni Łomnicki, in 1927 Banach received his own chair. Antoni Marian Łomnicki (b January 17, 1881 in Lwów (now Lviv - July 4, 1941 in Lemberg) (now Lviv was a Polish In 1924 he was also accepted as a member of the Polish Academy of Learning. The Polish Academy of Learning ( Polish: Polska Akademia Umiejętności) headquartered in Kraków, is one of two institutions in contemporary Poland having At the same time, from 1922, Banach also headed the second Chair of Mathematics at Lwów University. History Beginnings The University was founded on January 20 1661 when the King John II Casimir of Poland issued the diploma granting the city's

Scottish Café, Lwów
Scottish Café, Lwów

Young and talented, Banach gathered around him a large group of mathematicians. The Scottish Café (Kawiarnia Szkocka Шотла́ндська кав'я́рня Шотла́ндское кафе was the café in Lwów (now Lviv) where Lviv ( Ukrainian: Львів, L’viv, Lwów Lemberg Львов L'vov; see also other names) is a major city in western The group, meeting in the Scottish Café, soon gave birth to the "Lwów School of Mathematics. The Scottish Café (Kawiarnia Szkocka Шотла́ндська кав'я́рня Шотла́ндское кафе was the café in Lwów (now Lviv) where The Lwów School of Mathematics (lwowska szkoła matematyczna Львівська математична школа was a group of Mathematicians who worked between the " In 1929 the group began publishing its own journal, Studia Mathematica, devoted primarily to Banach's field of study — functional analysis. Studia Mathematica is a Polish Mathematics journal published since 1929. Around that time, Banach also began working on his best-known work, the first monograph on the general theory of linear-metric space. In Mathematics a linear space can mean one of two things In Linear algebra or Mathematical analysis, a Vector space In Mathematics, a metric space is a set where a notion of Distance (called a metric) between elements of the set is defined First published in Polish in 1931,[7] the following year it was also translated into French and gained wider recognition in European academic circles. [8] The book was also the first in a long series of mathematics monographs edited by Banach and his circle.

Banach's grave, Łyczaków Cemetery, Lviv
Banach's grave, Łyczaków Cemetery, Lviv

Following the invasion of Poland by Nazi Germany and the Soviet Union, Lwów came under the control of the Soviet Union. Lychakivskiy Cemetery (Cmentarz Łyczakowski Личаківський цвинтар translit Lviv ( Ukrainian: Львів, L’viv, Lwów Lemberg Львов L'vov; see also other names) is a major city in western The Invasion of Poland (1939 precipitated World War II. It was carried out by Nazi Germany, the Soviet Union, and a small German-allied Nazi Germany and the Third Reich are the common English names for Germany under the regime of Adolf Hitler and the National Socialist German Workers The Union of Soviet Socialist Republics (USSR was a constitutionally Socialist state that existed in Eurasia from 1922 to 1991 The Union of Soviet Socialist Republics (USSR was a constitutionally Socialist state that existed in Eurasia from 1922 to 1991 Banach, from 1939 a corresponding member of the Academy of Sciences of Ukraine, and on good terms with Soviet mathematicians, had to promise to learn Ukrainian to be allowed to keep his chair and continue his academic activities. The title Academician denotes a Full Member of an art literary or scientific Academy. The National Academy of Sciences of Ukraine (Національна академія наук України Natsional’na akademiya nauk Ukrayiny) is the highest state research The Union of Soviet Socialist Republics (USSR was a constitutionally Socialist state that existed in Eurasia from 1922 to 1991 [3] Following the German takeover of Lviv in 1941, all universities were closed and Banach, along with many colleagues and his son, was forced to eke out a living feeding lice with his blood at Professor Rudolf Weigl's Typhus Research Institute. Lice (singular louse) ( order Phthiraptera) are an order of over 3000 Species of wingless Insects three of which are classified Blood is a specialized Bodily fluid that delivers necessary substances to the body's cells such as nutrients and oxygen—and transports Waste products Professor Rudolf Stefan Weigl (1883 - 1957 was a famous Polish Biologist and inventor of the first effective Vaccine for Epidemic typhus. Typhus is any of several similar diseases caused by Louse -borne bacteria

After the Red Army captured Lvov in the Lvov-Sandomierz Offensive of 1944, Banach returned to the University and helped re-establish it after the war years. The Red Army ( Russian: Рабоче-Крестьянская Красная Армия R aboche- K rest'yanskaya K rasnaya A rmiya Lviv ( Ukrainian: Львів, L’viv, Lwów Lemberg Львов L'vov; see also other names) is a major city in western However, because the Soviets were removing Poles from annexed formerly-Polish territories, Banach began preparing to leave the city and settle in Kraków, Poland, where he had been promised a chair at the Jagiellonian University. Repatriation of Polish population in the years of 1944–1946 (also known as the first repatriation, to contrast with the ''second repatriation'' in the years 1955–1959 Kraków, in English also spelled Krakow or Cracow (ˈkrækaʊ M-W: krăk'ou krāk'ō is one of the largest and oldest cities in Poland Poland (Polska officially the Republic of Poland For several academies alternatively called "Krakow Academy" see Education in Kraków The Jagiellonian University (Uniwersytet [9] He was also considered a candidate for Minister of Education of Poland[4]. In January 1945, however, he was diagnosed with lung cancer and was allowed to stay in Lviv. He died on August 31, 1945, aged 53. Events 1056 - Byzantine Empress Theodora becomes ill dying suddenly a few days later without children to succeed the Throne Year 1945 ( MCMXLV) was a Common year starting on Monday (link will display the full calendar His funeral at the Lychakiv Cemetery turned into a patriotic demonstration by the Poles who still remained in the city[10]. Lychakivskiy Cemetery (Cmentarz Łyczakowski Личаківський цвинтар translit

Works

Banach's most influential work was Théorie des opérations linéaires (Theory of Linear Operations, 1932). In it he formulated the concept now known as "Banach space," and proved many fundamental theorems of functional analysis. In Mathematics, Banach spaces (ˈbanax named after Polish Mathematician Stefan Banach) are one of the central objects of study in Functional analysis For functional analysis as used in psychology see the Functional analysis (psychology article He was also one of the founders and editors of the journal, Studia Mathematica. Studia Mathematica is a Polish Mathematics journal published since 1929.

Besides being one of the founders of functional analysis, Banach also made important contributions to measure theory, set theory, and other branches of mathematics. In Mathematics the concept of a measure generalizes notions such as "length" "area" and "volume" (but not all of its applications have to do with

Quotes

Banach on a 1982 Polish postage stamp
Banach on a 1982 Polish postage stamp

Stanisław Marcin Ulam, another mathematician of the Lwów School of Mathematics, in his autobiography, attributes this to Banach:

"Good mathematicians see analogies. Poland (Polska officially the Republic of Poland A postage stamp is an adhesive paper evidence of pre-paying a fee for postal services Stanisław Marcin Ulam ( April 13, 1909 &ndash May 13, 1984) was a Polish Mathematician who participated in the Manhattan The Lwów School of Mathematics (lwowska szkoła matematyczna Львівська математична школа was a group of Mathematicians who worked between the Great mathematicians see analogies between analogies. "

Hugo Steinhaus said of Banach:

"An exceptional intellect, exceptional discoveries. Władysław Hugo Dionizy Steinhaus ( January 14, 1887 &ndash February 25, 1972) was a Polish Mathematician and . . he gave Polish science. . . more than anybody else. "

Hugo Steinhaus:

"Banach was my greatest scientific discovery. Władysław Hugo Dionizy Steinhaus ( January 14, 1887 &ndash February 25, 1972) was a Polish Mathematician and "

See also

References

In-line:
  1. ^ "new border "realignment" conferred Soviet citizenship on its new Polish inhabitants". In Mathematics, especially Functional analysis, a Banach algebra, named after Stefan Banach, is an Associative algebra A over the The Banach Fixed point theorem (also known as the contraction mapping theorem or contraction mapping principle) is an important tool in the theory of In Functional analysis, the open mapping theorem, also known as the Banach-Schauder theorem, is a fundamental result which states that if a continuous In Functional analysis and related branches of Mathematics, the Banach–Alaoglu theorem (also known as Alaoglu's theorem) states that the closed [1]
  2. ^ a b c (Polish) Monika Waksmundzka-Hajnos (2006). Wspomnienie o Stefanie Greczku. Wortal Stefana Banacha. Gdańsk University. Retrieved on 2007-02-22. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1495 - King Charles VIII of France enters Naples to claim the city's throne
  3. ^ (English) Roman Kałuża (1996). Through a Reporter's Eyes: the life of Stefan Banach, 137. ISBN 0817643710.  
  4. ^ Roman Kałuża, op. cit. , p. 13
  5. ^ Roman Kałuża, op. cit. , p. 16
  6. ^ (French) (Polish) Stefan Banach (1922). "Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales". Fundamenta Mathematicae III.  
  7. ^ Stefan Banach: Teoria operacji liniowych.
  8. ^ (French) Stefan Banach: Théorie des opérations linéaires (Theory of Linear Operations).
  9. ^ [2]Banach biography on The MacTutor History of Mathematics archive.
  10. ^ Tadeusz Krzyżewski, as cited in: (Polish) Stanisław Kosiedowski. Stefan Banach. Mój Lwów. Retrieved on 2008-05-20. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 325 - The First Council of Nicaea &ndash the first Ecumenical Council of the Christian Church is held

External links

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