vix.ing · top · new · best · stats · spec

A theorem of Krein revisited

2002/09/24 by Timur Oikhberg, Oikhberg, Timur, Vladimir G. Troitsky +1
Mathematics · #46B40 #47B60 #47B65 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory in Mathematical Physics #math.FA #msc:46B40 #msc:47B60 #msc:47B65

paper · pdf · doi:10.48550/arxiv.math/0209331

To appear in Rocky Mountain J. Math

arxiv created 2002/09/24 · openalex publication_date 2002/09/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

M. Krein proved in 1948 that if T is a continuous operator on a normed space leaving invariant an open cone, then its adjoint T* has an eigenvector. We present generalizations of this result as well as some applications to C*-algebras, operators on l1, operators with invariant sets, contractions on Banach lattices, the Invariant Subspace Problem, and von Neumann algebras.

Related