Per Enflo

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Per Enflo (1972)

Per Enflo ( pronunciation : [ ˌpæːɹ ˈeːnfluː ], born May 30, 1944 in Stockholm ) is a Swedish mathematician and university professor at Kent State University in Ohio, USA. He is known for solving some fundamental problems in functional analysis (theory of Banach spaces ).

Life

Enflo is one of five children of a surveyor and actress. As a child, he was gifted in both math and music. In 1956 and 1961 he won the Swedish national piano competitions for young people and made his debut as a solo pianist with the Royal Swedish Opera Orchestra at the age of twelve. In addition to piano, he also studied composition and conducting and continued to perform in public regularly in the 2000s. In 1999 he took part in the first international van Cliburn competition for amateur concert pianists.

Enflo studied mathematics at Stockholm University , where he received his PhD in 1970 from Hans Rådström on the infinite dimensional version of Hilbert's fifth problem ( Investigations on Hilbert's fifth problem for non locally compact groups ). He was then at the Universities of Stockholm, the University of California, Berkeley , Stanford University , the École polytechnique ( Paris ), the Mittag-Leffler Institute , the Royal Technical University in Stockholm and the Ohio State University . He is a professor at Kent State University , holding the title University Professor since 1989 . In 1975 he received a research grant from the Alfred P. Sloan Foundation ( Sloan Research Fellowship ).

plant

Enflo became known for solving some 40 years of unsolved problems in functional analysis. Stanisław Mazur asked in the Scottish Book (Problem # 153) whether every separable Banach space has a shudder base . Alexander Grothendieck later associated this with the so-called approximation property of Banach spaces, i.e. with the question of whether every compact operator in every Banach space is a limit value of operators of finite order. Enflo answered both problems negatively - he constructed a separable Banach space in which neither the approximation property nor a shudder basis exists. Stanisław Mazur originally donated a goose as prize money based on a proposal by Stefan Banach in 1936, which Mazur then presented to Enflo in a festive ceremony in 1972. Enflo had been working on the proof since 1967, developing new methods that were used in other areas of mathematics.

In 1975 he solved another fundamental long open problem of the theory of Banach spaces, the problem of invariant subspaces in Banach spaces. He solved it in a negative sense, that is, he showed the existence of a linear bounded operator with no invariant nontrivial subspace in a Banach space. He published the sketch of the proof in 1976 in Laurent Schwartz and Maurey's seminar at the Ecole Polytechnique; the complete proof circulated as a manuscript for over a decade and was only published in 1987. He worked on the complex proof from 1970 to 1975, and here, too, the methods found applications in other areas of mathematics such as the development of algorithms for polynomial factorization. Even after that, Enflo worked on other aspects of the problem of invariant subspaces such as the still open Hilbert space version.

In 1974 he was invited speaker at the International Congress of Mathematicians in Vancouver (Recent results on general Banach spaces).

Enflo also looked at population genetics, such as whether the populations of Neanderthals and Homo sapiens have mixed up.

Web links

Individual evidence

  1. ↑ Birth dates according to biography in Karen Saxe: Beginning Functional Analysis. Undergraduate Texts in Mathematics, Springer Verlag 2001, p. 123.
  2. ↑ Per Enflo in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / name used
  3. ↑ Per Enflo: A counterexample to the approximation problem in Banach spaces. In: Acta Mathematica . Volume 130, No. 1, July 1973, pp. 309-317.
  4. ↑ See: Kawiarnia Szkocka .
  5. ^ Enflo: On the invariant subspace problem for Banach spaces. Acta Mathematica, Vol. 158, 1987, pp. 213-313.
  6. ↑ Simplified in: B. Beauzamy: Un opérateur sans sous-espace invariant: simplification de l'exemple de P. Enflo. Integral Equations and Operator Theory, Volume 8, 1985, pp. 314-384.
  7. ↑ P. Enflo, John D. Hawks, M. Wolpoff: A simple reason why Neanderthal ancestry can be consistent with current DNA information. American Journal Physical Anthropology, 2001.
personal data
SURNAME Enflo, Per
BRIEF DESCRIPTION Swedish mathematician and university professor
DATE OF BIRTH May 30, 1944
PLACE OF BIRTH Stockholm