English

Local Definitizability of $T^{[*]}T$ and $TT^{[*]}$

Spectral Theory 2010-05-02 v1 Functional Analysis

Abstract

The spectral properties of two products ABAB and BABA of possibly unbounded operators AA and BB in a Banach space are considered. The results are applied in the comparison of local spectral properties of the operators T[]TT^{[*]} T and TT[]TT^{[*]} in a Krein space. It is shown that under the assumption that both operators T[]TT^{[*]} T and T[]T^{[*]} have non-empty resolvent sets, the operator T[]TT^{[*]} T is locally definitizable if and only if TT[]TT^{[*]} is. In this context the critical points of both operators are compared.

Keywords

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}
}