Local Definitizability of $T^{[*]}T$ and $TT^{[*]}$
Spectral Theory
2010-05-02 v1 Functional Analysis
Abstract
The spectral properties of two products and of possibly unbounded operators and in a Banach space are considered. The results are applied in the comparison of local spectral properties of the operators and in a Krein space. It is shown that under the assumption that both operators and have non-empty resolvent sets, the operator is locally definitizable if and only if is. In this context the critical points of both operators are compared.
Cite
@article{arxiv.1004.1584,
title = {Local Definitizability of $T^{[*]}T$ and $TT^{[*]}$},
author = {Friedrich Philipp and André C. M. Ran and Michał Wojtylak},
journal= {arXiv preprint arXiv:1004.1584},
year = {2010}
}