Nachman Aronszajn

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Nachman Aronszajn (born July 26, 1907 in Warsaw , † February 5, 1980 in Corvallis , Oregon ) was a Polish-American mathematician who dealt with analysis and mathematical logic.

Life

Aronszajn studied at the University of Warsaw , where he received his doctorate in 1930 with Stefan Mazurkiewicz , and he received his doctorate a second time in 1935 at the Sorbonne with Maurice Fréchet . He was in France from 1930 to 1940 (which he had to leave as a Jew under German occupation), from 1940 to 1945 in England, then again until 1948 in France and went to the USA in 1948. He taught at Oklahoma State University - Stillwater (then Oklahoma Agricultural and Mechanical University), but left after Ainsley University dismissed Diamond because he refused to take an oath of loyalty. He went to the University of Kansas with Diamond in 1951 and was a professor there from 1951. In 1977 he retired. He was then an adjunct professor at the University of Oregon at Corvallis.

He is known, among other things, for a theorem with Kennan T. Smith that every compact operator in a Banach space of two or more dimensions has an invariant subspace. In functional analysis, he and Stefan Bergman developed the theory of Hilbert spaces with a reproducing core (theorem of Aronszajn and Moore ).

In set theory, the Aronszajn tree is named after him, a tree with uncountably many nodes, but in which branches and levels cannot be uncountable. Aronszajn constructed such a tree in 1934.

With Prom Panitchpakdi , he introduced injective metric spaces (also called hyperconvex metric spaces).

Fonts

  • Theory of Reproducing Kernels, Transactions of the American Mathematical Society, Volume 68, 1950, pp. 337-404.
  • with KT Smith: Invariant subspaces of completely continuous operators, Annals of Mathematics, Volume 60, 1954, pp. 345-350
  • with P. Panitchpakdi: Extensions of uniformly continuous transformations and hyperconvex metric spaces, Pacific Journal of Mathematics, Volume 6, 1956, pp. 405-439, Correction Volume 7, 1957, p. 1729
  • Sur les décompositions des fonctions analytiques uniformes et sur leurs applications, Acta Mathematica, 65, 1935, 1–156

literature

  • Pawel Szeptycki, Nachman Aronszajn (1907-1980), Wiadom Mat., 25, 1983, 89-96
  • Szeptycki, Rocky Mountain J. Math., 10, 1980, 1–6 (publications by Aronszajn)

Web links

Individual evidence

  1. ↑ Biography after Jean A. Larson Infinite Combinatorics , in: Dov Gabbay, Akihiro Kanamori, John Woods (Eds.): Handbook of the History of Logic, Volume 6, North Holland 2012, p. 189. There are further references.
  2. ↑ Published by Đuro Kurepa , Ensembles ordonnés et ramifiés, Publ. Math. Univ. Belgrade 4 (1935), 1-138 (dissertation with Frechet), Ensembles lineaires et une classe de tableaux ramifies (Tableaux ramifies de M. Aronszajn), Publ. Math. Univ. Belgrade 6/7 (1937/38), 129-160 (reprinted in Kurepa, Selected Papers, Belgrad 1996). Kurepa introduces the term Suslin tree in addition to the term Aronszajn tree. According to Pawel Szeptycki , Aronszajn constructed the tree named after him to close a gap in Kurepa's work.
personal data
SURNAME Aronszajn, Nachman
BRIEF DESCRIPTION Polish-American mathematician
DATE OF BIRTH July 26, 1907
PLACE OF BIRTH Warsaw
DATE OF DEATH 5th February 1980
Place of death Corvallis , Oregon