Per Enflo

Per Enflo ( pronunciation: [ ˌ Pae e ː ː ɹ nflu ː ], * May 30, 1944 in Stockholm) is a Swedish mathematician and professor at Kent State University in Ohio, USA. He is known for solving some fundamental problems of functional analysis ( theory of Banach spaces ).

Life

Enflo is one of five children of a surveyor and an actress. He was early gifted as a child both in mathematics and in music. 1956 and 1961, he won the Swedish national piano competitions for youth and made ​​his debut as a solo pianist with twelve years with the Royal Swedish Opera Orchestra. He studied piano and composition and conducting in addition and also appeared in the 2000s still regularly publicly. In 1999 he participated in the first international Van Cliburn Competition for amateur concert pianist in part.

Enflo studied mathematics at Stockholm University, where he received his doctorate in 1970 with Hans Rådström on the infinite-dimensional version of Hilbert's fifth problem ( Investigations on Hilbert 's fifth problem- locally compact groups for non ). 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, 1989 University with the title of Professor.

Work

Enflo became known for solving some about 40 years of unsolved problems of functional analysis. Stanisław Mazur presented in the Scottish Book ( Issue # 153) the question whether every separable Banach space has a Schauder basis. Later, it was brought by the Alexander Grothendieck with the so-called approximation property of Banach spaces in connection, that is the question of whether every Banach space every compact operator is limit of operators of finite rank. Enflo responded negatively both problems - he constructed a separable Banach space, in which neither the approximation property is still exists a Schauder basis. Stanisław Mazur had it originally in 1936 as a goose prize sponsored by the proposal of Stefan Banach, who was then also Enflo 1972 presented by Mazur in a solemn ceremony. On the evidence Enflo had worked since 1967, and he developed this new methods that have been applied in other areas of mathematics.

In 1975, he broke 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 without nontrivial invariant subspace in a Banach space. The sketch of the proof he published in 1976 at the seminar of Laurent Schwartz and Maurey the Ecole Polytechnique, the complete proof circulated over a decade as a manuscript and was not published until 1987. He worked on the complex evidence from 1970 to 1975, and also the methods found applications in other areas of mathematics such as in the development of algorithms for polynomial factorization. Even after Enflo worked on other aspects of the problem of invariant subspaces 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, for example, the question of whether the populations of Neanderthals and Homo Sapiens have mixed.