Interdisciplinary Mathematics Institute (IMI)

25 de mayo de 2023.Boletín del IMI.

A potential definitive answer to the invariant subspace problem in Hilbert spaces. Prof. Per H. Enflo (Kent State University, USA) has just announced via his collaborators from the Interdisciplinary Mathematics Institute (IMI) that he might have just potentially solved the long standing Invariant Subspace Problem in Hilbert Spaces

On the invariant subspace problem in Hilbert spaces

Available online >> arXiv:2305.15442 [pdf,ps,other]

Authors: Per H. Enflo

Abstract:  In this paper we show that every bounded linear operator T on a Hilbert space H has a closed non-trivial invariant subspace.

Submitted 24 May, 2023;originally announced May 2023.

Comments:13 pages

MSC Class:47A15; 47B02

A history of solving some famous problems in mathematical analysis

This paper provides a historical view of what functional analysis is, a biography of Per H. Enflo and a short view of four fundamental problems in the geometry of Banach spaces.

It gives the story of how Enflo, after several years of work, managed to solve three of these problems. It is a story of trying many ideas, testing them on simpler problems, trying to combine different techniques for handling different aspects of the problems, making many failed attempts and finally succeeding.

In 1966 Enflo found a general strategy for solving many problems in infinite dimensions, by combining appropriate finite-dimensional techniques with induction procedures. When applied to the old, fundamental problems in functional analysis, this has led to new concepts, problems, techniques and results in analysis. These developments have been applied also in several other areas of mathematics and computer science.

Department of Mathematical Sciences, Kent State University, Kent, OH, USA
Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Mashhad, Iran
Instituto de Matemática Interdisciplinar (IMI), Facultad de Ciencias Matemáticas, Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, Madrid, Spain

When did you make the decision to go into math instead of music?

I have never made, and will never make, any such decision

  • Mathematics and Music - What is the connection? Lecture > 31 August 2021, Science Festival Strömstad Academy Slides
  • Beethoven last piano sonata > Strömstad Academy's Scientific Festival 2021
  • Mozart  Beethoven  Chopin > Jubilee Congress of Polish Mathematicians on the 100th Anniversary of Polish Mathematical Society (2019, Krakow)
  • Lecture December 2021  Slides >> to Holiday Lecture by Per Enflo  via Zoom - Jani Virtanen (Reading and Helsinki) & Håkan Hedenmalm (KTH and Reading) Lecture by Per Enflo: An infinite-dimensional version of Hilbert's fifth problem with connections to non-linear geometry of Banach spaces

Mathematics >>     Music >>     Interviews & Reviews >>

Per Enflo - mathematician and pianist - was the last laureate of a prize

for solving a scientific problem from the Scottish Book.

Contact  +46(0)721-808 870       per.enflo at gmail.com       www.perenflo.com © 2011