A theorem of Krein revisited
Functional Analysis
2007-05-23 v1
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 l_1, operators with invariant sets, contractions on Banach lattices, the Invariant Subspace Problem, and von Neumann algebras.
Cite
@article{arxiv.math/0209331,
title = {A theorem of Krein revisited},
author = {Timur Oikhberg and Vladimir G. Troitsky},
journal= {arXiv preprint arXiv:math/0209331},
year = {2007}
}
Comments
To appear in Rocky Mountain J. Math