# Stefan Banach

Stefan Banach ( stɛfan Banax / i;? Born March 30, 1892 in Krakow, † August 31, 1945 in Lviv ) was a Polish mathematician. He is considered the founder of modern functional analysis and as one of the main representatives of the Lviv mathematicians school.

## Life

Banachs father was Stefan Greczek (which is not fully secured ), his mother Katarzyna Banach, who was not married to Stefan Greczek. He grew up in a foster family on ( at Franciszka Płowa and her daughter, Maria Puchalska ). From 1902 to 1910 he attended the Fourth Gymnasium in Krakow.

After leaving school he worked in a bookshop Cracow and studied at the same time a self-taught mathematics. Between 1911 and 1913 he was a student at the Polytechnic Institute in Lvov, where he took part exam from the so-called half- degree ( bachelor's degree ).

After the outbreak of the First World War he worked as a guard at the road. For the military service, he was disabled due to his short-sightedness. After returning to Krakow, he earned his living by tutoring. He continued to study mathematics on his own. In 1916 the mathematician Hugo Steinhaus Stefan Banach met and began to care for him. Your acquaintance resulted in a joint publication and long-term cooperation. After its initial publication Banach filed a steadily more mathematical work. By Stone House ' efforts Banach received from 1920 to 1922, a Research Associate position at Antoni Łomnicki the chair of mathematics in the Department of Mechanics of the Polytechnic Lviv. In 1922, he presented at the Jan Kazimierz University in Lvov his doctoral examination. The title of his dissertation was " Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales " ( About operations in abstract quantities and its application to integral equations, Fundamenta Mathematicae 3, 1922). With the fundamental records that contains this work, he created a new area of mathematics, the Functional Analysis.

He habilitated in 1922 at the University of Lviv ( decision of the Department of the Council of 30 June) and was there on 22 July of the same year an associate professor. In 1927 he became a full professor. Between 1922 and 1939 he was the owner of the second chair of mathematics at the University of Lemberg. He was there as an eccentric: instead of working in his office, Banach usually sat in the local 'Scottish Café " to fill his notebooks with ideas for functional analysis - therefore carry his notes from that time the name " Scottish Notebooks ". In 1924 he became a corresponding member of the Polish Academy of Sciences, from 1931 he was a regular member of the Warsaw Scientific Society. In the Scientific Society Lemberg he was adopted from 1923, from 1927 active member. From 1932 to 1936 he was Vice President, 1939-1945 President of the Polish Mathematical Society, he was one of the founding members in 1919.

In 1930 he was awarded the Science Prize of the city of Lviv. In the years 1936-1939 he was Vice President of the Mathematical Committee of the Council for exact and applied sciences. In 1936 he gave a plenary lecture at the International Congress of Mathematicians in Oslo ( " The theory of operations and their importance for the analysis" ). 1939 awarded him the Polish Academy of Sciences for their great price.

After the invasion of the Red Army in the same year he became a corresponding member of the Academy of Sciences of the Ukrainian Soviet Socialist Republic and stayed at the Lviv University as holder of the first Chair of Mathematical Analysis and Dean of the Faculty of Mathematics and Physics of the University ( 1939-1941 ).

During the German occupation he had the livelihood for himself and his wife Łucja and his son Stefan (later a well-known neurosurgeon ) earn by donating to Rudolf Weigl's Institute of Bacteriology blood for feeding lice, which were then used for typhus experiments.

After the Red Army had occupied Lviv again in 1944, he became professor of mathematics again. On 31 August 1945 he died in Lviv on lung cancer and was buried at the Riedl - monument on the Lychakiv Cemetery in Lviv.

## Honors

- The Polish Mathematical Society in 1946 created the scientific Stefan Banach Prize in his honor.
- In university towns, streets were named after him.
- In 1972, the International Banach Center for Mathematics, based in Warsaw was founded.
- 2012 was the National Bank of Poland in his honor a coin Nominalwertvon 200, - zloty out.

## Work

He dedicated his first work, among others, the Fourier series. In the first co-authored with stone house work, he treated the question of the convergence in the mean of the partial sums of a Fourier series and was able to answer definitively negative. He also worked on orthogonal functions and series, the Maxwell equations, derivatives of measurable functions and measure theory.

In his doctoral thesis and in the monograph " Théorie des opérations linéaires " (Theory of linear operations ), he defined axiomatically those spaces that were later named after him, the Banach spaces. Stefan Banach put the final bases for functional analysis and proved many fundamental sets, such as the Hahn- Banach theorem, the fixed point theorem of Banach and Banach - Steinhaus. He led the appropriate terminology, which is binding on the whole world in the functional analysis today, and gave the first lecture in this area.

In 1924 he put together with his Polish counterpart Alfred Tarski a sentence that became famous as the Banach - Tarski paradox, an important contribution to set theory.

Banach wrote over sixty scientific papers and found numerous new theorems, which proved to be of fundamental importance in many areas of mathematics. Banachs work style, his extraordinary scientific intuition, his directness and openness allowed him to found together with stone house, the mathematical school of Lviv.

Banach was an excellent teacher and was also the author of many textbooks, including even textbooks for secondary schools.

## Named after Stefan Banach

The following terms are named after Stefan Banach:

- Banach algebra
- Banach space
- Banach
- Banachlimes
- Banach - Alaoglu
- Hahn- Banach
- Banach mapping theorem
- Banach fixed point theorem
- Banach - Mackey
- Banach - Mazur
- Banach - Mazur distance
- Banach - Saks property
- Banach - Schauder
- Banach - Steinhaus
- Banach - Tarski paradox
- International Banach Center for Mathematics
- Stefan Banach Medal
- Stefan Banach Prize