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Topic: Stefan Banach

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Banach algebra

Stanislaw Mazur

Banach space

Hahn Banach theorem

Lvov school of mathematics

Hugo Steinhaus

Wladyslaw Orlicz

Ulam

List of lists of mathematical topics

Topological space

Normed vector space

Witold Hurewicz

Karol Borsuk

Alfred Tarski

Kazimierz Zarankiewicz

	Stefan Banach - Wikipedia, the free encyclopedia
		Stefan Banach (March 30, 1892 in Kraków, Austria-Hungary now Poland– August 31, 1945 in Lwów, Soviet Union - occupied Poland), was an eminent Polish mathematician, one of the moving spirits of the Lwów School of Mathematics in pre-war Poland.
		When World War II began, Banach was President of the Polish Mathematical Society and a full professor of University of Lwów.
		Banach survived the subsequent brutal German occupation from July 1941 up to February 1944, earning a living by feeding lice with his blood in the Typhus Research Institute of Prof.
	en.wikipedia.org /wiki/Stefan_Banach (329 words)

	Stefan Banach
		Stefan Banach (March 30 1892 - August 31 1945), a Polish mathematician, one of the moving spirits of the Lvov school of mathematics in pre-war Poland (see: Lviv).
		Banach survived, but the only way he could work for a living was by feeding lice with his blood in a German institute where typhoid fever research was conducted.
		Banach was the founder of functional analysis; he also made important contributions to the theory of vector spaces, measure theory, set theory and other branches of mathematics.
	www.guajara.com /wiki/en/wikipedia/s/st/stefan_banach.html (268 words)

	Banach space - Wikipedia, the free encyclopedia
		In mathematics, Banach spaces, named after Stefan Banach who studied them, are one of the central objects of study in functional analysis.
		Banach spaces are defined as complete normed vector spaces.
		If V is a Banach space and K is the underlying field (either the real or the complex numbers), then K is itself a Banach space (using the absolute value as norm) and we can define the dual space V′ as V′ = L(V, K), the space of continuous linear maps into K.
	en.wikipedia.org /wiki/Banach_space (1294 words)

	Stefan Banach
		Banach proved a number of fundamental results on normed linear spaces, and many important theorems are today named after him.
		Banach had been on good terms with the Soviet mathematicians before the war started, and he was treated well by the new Soviet administration.
		Banach planned to go to Kraków after the war to take up the chair of mathematics at the Jagiellonian University, but he died in Lvov in 1945 of lung cancer.
	www.stetson.edu /~efriedma/periodictable/html/Bh.html (806 words)

	[No title]
		After the Soviets invaded Lwow in 1939, Banach was allowed to continue to hold his chair at the university and he became the Dean of the Faculty of Science, the university being renamed the Ivan Franko University.
		Banach died of lung cancer in Lwow in 1945.
		Banach founded the important modern mathematical field of functional analysis and made major contributions to the theory of topological vector spaces.
	www.angelfire.com /scifi2/rsolecki/stefan_banach.html (735 words)

	[No title]
		As noted above, Janiszewski, along with Stefan Banach, Waclaw Sierpinski, and Stanislaw Zaremba were all instrumental in the development of the Polish School of Mathematics; Poland issued stamps in their honor on the occasion of the 1982 International Congress of Mathematicians, actually held in Warsaw in 1983.
		Banach had a strong, but eccentric, personality; he hardly ever wrote letters and never addressed questions addressed to him by post, but in person he was a vibrant and energetic participant in mathematical discussions.
		Banach's physical condition greatly deteriorated during World War II; this partly was due to the general famine, but also due his job as a lice feeder at he Rudolf Weigl Bacteriological Institute.
	www.math.wfu.edu /~kuz/Stamps/PolishSchool/PolishSchool.htm (2628 words)

	Search Results for Banach
		In 1972 the International Stefan Banach Centre was established as part of the Institute of Mathematics of the Polish Academy of Sciences.
		K Szalajko, Reminiscences of Stefan Banach against the background of Lvov and the Lvovian school of mathematics (Polish), Opuscula Math.
		Banach is awarded his habilitation for a thesis on measure theory.
	www-groups.dcs.st-and.ac.uk /~history/Search/historysearch.cgi?SUGGESTION=Banach&CONTEXT=1 (787 words)

	Short biography of Stefan Banach by Waclaw Szybalski and Stanislaw Kosiedowski
		Banach's father had never given his son much support, but now once he left school he quite openly told Banach that he was now on his own.
		Banach had been on good terms with the Soviet mathematicians before the war started, visiting Moscow several times, and he was treated well by the new Soviet administration.
		Banach planned to go to Kraków after the war to take up the chair of mathematics at the Jagiellonian University but he died in Lwów in 1945 of lung cancer.
	wwwzenger.informatik.tu-muenchen.de /~huckle/szyb.htm (1282 words)

	Stefan Banach, Mathematician
		Stefan Banach, son of Stefan Greczek, a tax official and, possibly, of Katarzyna Banach.
		Banach was brought up in Krakow by Franciszka Plowa and received his early education from a French intellectual, Juliusz Mien, who was the guardian of Plowa’s daughter.
		In 1902, Banach finished primary school in Krakow and began his secondary education at the Henryk Sienkiewicz Gymnasium No. 4 in the same city.
	www.polishwashington.com /prominent-poles/stefan.banach.htm (740 words)

	History of Operator Theory (Site not responding. Last check: 2007-10-21)
		In the first textbook on operator theory, Théorie des Opérations Linéaires, published in Warsaw 1932, Stefan Banach states that the subject of the book is the study of functions on spaces of infinite dimension, especially those he coyly refers to as spaces of type B, otherwise Banach spaces (definition).
		Perhaps if Banach had had access to the internet he wouldn't have so carelessly reduced his historical remarks in the introduction to an unsupported repetition of Jacques Hadamard's assertion that it was mainly the creation of Vito Volterra.
		Stefan Banach, in which geometric language was used throughout.
	www.mathphysics.com /opthy/OpHistory.html (2635 words)

	Banach Stefan: Free Encyclopedia Articles at Questia.com Online Library (Site not responding. Last check: 2007-10-21)
		Famous kings, such as Stefan Batory (1575-86) and Jan Sobieski III (1674-96), and great landowning families, the Lubomirskis, Radziwills, Zamoyskis, Czartoryskis...
		Colonel Stefan Rowecki, based in Warsaw, was given the equivalent appointment...underground movement were: the Socialist Kazimierz Puzak; Stefan Korbofiski who represented the Peasants; Aleksander D 032bski...
		This theorem, which Tarski and another Polish mathematician, Stefan Banach, arrived at independently, states that a solid ball of any given size (a pea, for example) can be decomposed into pieces...
	www.questia.com /library/encyclopedia/banach-stefan.jsp?l=B&p=1 (708 words)

	The Life of Stefan Banach
		Before capturing the Polish university town of Lvov, where Banach lived and worked, German officials compiled a list of prominent professors, scientists, and writers in Lvov who would be executed.
		An alert reader will wonder why Banach, who at this time was President of the Polish Mathematical Society and a Dean at the university, was not among the intellectuals marked down for liquidation.
		Banach himself was "somewhat strange" and "eccentric"; that description surely fits many mathematicians.
	www.axler.net /Banach.html (1048 words)

	Banach Coat of Arms (Site not responding. Last check: 2007-10-21)
		The German surname Banach emerged in the lands that formed the powerful German state of Prussia, which at one time was an immense German territory that stretched from France and the Low Countries to the Baltic sea and Poland.
		The borders of the Barbarian kingdoms changed frequently, but the region that became known as Prussia was roughly divided between the areas of Brandenburg-Prussia, West Prussia, and East Prussia.
		West Prussia, where the distinguished surname Banach was born, was nestled between Brandenburg and East Prussia on the Vistula River.
	www.houseofnames.com /xq/asp.c/qx/banach-coat-arms.htm (1995 words)

	William Timothy Gowers (Site not responding. Last check: 2007-10-21)
		Gowers has been able to utilize complicated mathematical constructions to prove some of the conjectures of the Polish mathematician Stefan Banach (1892-1945), including the problem of "unconditional bases." Banach was an eccentric, preferring to spend his time in the café rather than in his office in the University of Lvov.
		Banach spaces are sets whose members are not numbers but complicated mathematical objects such as functions or operators.
		However, in a Banach space it is possible to manipulate these objects like numbers.
	www.ams.org /featurecolumn/archive/gowers.html (333 words)

	Waclaw Szybalski: The genius of Rudolf Stefan Weigl (1883-1957), a Lvovian microbe hunter and and breeder - In Memoriam
		Rudolf Stefan Weigl(1883-1957) at the University of Jan Kazimierz (UJK) in Lwów, Poland (Weigl, 1920, 1930a,b, 1947).
		It is a pity that Stefan Szybalski has not written up his memoirs of this period, since many famous Russian professors and Academicians, who were 'starved' of the contacts with the Western world made a pilgrimage to Weigl's Institute in Lwów, considered by Russian as a Vienna-like Western European city, though occupied then by Soviets.
		In: A Monograph "Rudolf Stefan Weigl (1883-1957)" pp.
	lwow.home.pl /weigl/in-memoriam.html (7178 words)

	Stefan Banach Biography / Biography of Stefan Banach 1900 To 1949: Mathematics Biography
		Banach was born in 1892 in Krakow, Austria-Hungary, which is now Poland.
		When he had completed his schooling in Krakow, he decided to abandon his study of mathematics for other subjects, but they did not hold much appeal, so he soon returned to lecture in mathematics at the Institute of Technology in Lvov and later became a professor at the University of Lvov.
		Banach is known as the founder of modern functional analysis, but his other specialties also brought him a measure of fame: the theory of topological vector space, and what is today known as Banach space as well as Banach algebras.
	www.bookrags.com /biography-stefan-banach-scit-06123 (182 words)

	American Mathematical Monthly: June-July, 1997
		Let X and Y be real Banach spaces and let f be a map from X to Y such that f (0) = 0.
		It is known that if f is such a map between real Banach spaces, if f(0) = 0, and if f is surjective, then there exists a linear isometry g such that f and g are uniformly close.
		This was proved in 1945 by Hyers and Ulam for the special case of Hilbert spaces, and then extended to Banach spaces over the years by several authors.
	www.maa.org /pubs/monthly_june97_toc.html (916 words)

	Isoperimetric, Banach, Area, Crystals (Site not responding. Last check: 2007-10-21)
		A Banach style area can now be defined as the integral of norm of small area elements.
		I conjecture that if we take a crystal centered at the origin as the unit ball of a Banach space, then the shape for constant volume that minimizes the Banach style area is similar and parallel to the crystal itself.
		Stefan Banach contributed to the problem of the definition of area in Euclidean space and so "Banach Area" may be a confusing term.
	www.cap-lore.com /MathPhys/crystal.html (557 words)

	AllRefer.com - Stefan Banach (Mathematics, Biography) - Encyclopedia
		Stefan Banach[ste´fAn bA´nAkh] Pronunciation Key, 1892–1945, Polish mathematician.
		He was educated at the Institute of Technology in Lviv; his doctoral thesis laid the foundations of modern functional analysis, which he continued to work at throughout his life.
		He also made fundamental contributions to general topology, set theory, the theory of measure and integration, and the general theory of linear spaces, or vector spaces, e.g., ThEorie des opErations linEaires (1932).
	reference.allrefer.com /encyclopedia/B/Banach-S.html (186 words)

	MATHSTAT@MEMPHIS.edu (Site not responding. Last check: 2007-10-21)
		During the week of October 5-9, 2001, the international research conference "TRENDS IN BANACH SPACES and OPERATOR THEORY" was held on the campus of the University of Memphis.
		Moderated by professor Sheldon Axler from San Francisco University, it is fair to say that during the session, in non-typical fashion (for mathematics conferences), the discussion was spirited, bordering on rowdy, and many of the speakers from both the panel and the audience emphasized multiple applications of this traditionally "pure" mathematical theory.
		The theories of Banach Spaces and Linear Operators are intimately related, and they lie at the core of applications in such diverse fields as Differential Equations, Dynamical Systems, Financial Mathematics, and many other fields in mathematics.
	www.msci.memphis.edu /newscol7.html (784 words)

	polish consulate in sheffield (Site not responding. Last check: 2007-10-21)
		Born in Krakow, Stefan Banach studied mathematics at the Jagiellonian University there.
		A Banach space is a real or complex normed vector space that is complete as a metric space under the metric
		There is the Hahan-Banach theorem, Banach-Steinhaus theorem, the Banach-Alaoglu theorem, the Banach fixed-point theorem and the Banach-Tarski paradoxical decomposition of a ball.
	www.shef.ac.uk /uni/projects/pc/page31.html (153 words)

	legendsscience
		The soul, on the other hand, was personified by Stefan Banach at the University of Lwow (commonly known as the Lwow School), a part of Poland during the inter-war period.
		Banach's work and that of his students, such as Mazur, Orlicz, Schauder, and Ulam created the field of mathematics known as "Functional Analysis," the mathematics of the nuclear age.
		Even though Banach and Sierpinski are now deceased, their light continues to illuminate mathematicians and, ultimately, all of us.
	www.polamjournal.com /Library/Biographies/legendsscience/legendsscience.html (1778 words)

	Atlas: Stefan Banach and the Weigl Institute: Banach During World War II by Daniel Alexander (Site not responding. Last check: 2007-10-21)
		The record of Stefan Banach's experience during World War II is slim.
		Banach's story is intimately linked to that of the relatively unknown "Schindleresque" factory owner who employed Banach, Rudolf Weigl, creator of the typhus vaccine, who in 2003 was honored by Yad Vashem as Righteous Among the Nations.
		Banach's mathematics will not be discussed, except in very broad terms.
	atlas-conferences.com /cgi-bin/abstract/caql-75 (233 words)

	References for Banach (Site not responding. Last check: 2007-10-21)
		E Marczewski, Sur l'oeuvre scientifique de Stefan Banach II.
		W Orlicz, Sur l'oeuvre scientifique de Stefan Banach I. Théorie des opérations et théorie des séries orthogonales, Colloquium Math.
		H Steinhaus, Stefan Banach, Studia Mathematica 1 (1963), 7-15.
	www-gap.dcs.st-and.ac.uk /~history/References/Banach.html (194 words)

	Alibris: Banach
		From basic sketching and modeling through advanced modeling techniques, Autodesk Inventor« 6: Essentials is a must for students, mechanical engineers, and others who want to learn how to take maximum advantage of this powerful design tool.
		From basic sketching and modeling through advanced modeling techniques, Autodesk Inventor 6 Essentials with Autodesk Inventor 7 UPDATE is a "must" for students, mechanical engineers, and others who want to learn how to take maximum advantage of this powerful design tool.
		Banach guides board members through a strategic plan to analyze the existing board structure, create a plan, execute it, and evaluate the results.
	www.alibris.com /search/books/author/Banach (1011 words)

	Banach Center studies functional analysis with the best
		Stefan Banach, who the center is named after, is said to be among the most brilliant mathematicians of the 20th century and the developer of fundamental analysis.
		But a goose is not all Enflo got - he is having two biographies written about him because of his contributions to this field, which will be used in under and upper graduate studies.
		He said when the university realized how prominent this field and its professors were becoming, they knew they had to take advantage of the success.
	www.stater.kent.edu /stories_old/00fall/92900/P928mathmaticiansLD.html (840 words)

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