Local spectral properties on skew diagonal operator matrices
Abstract
Let T∈L(H) be similar to −T via an involution U. In this paper, we study the local spectral properties of T. Furthermore, if the operator TA is in the class (S) in the sense of N. Salinas [Invariant subspaces and operators of class S. Pacific J Math. 1972;42(2):497–513.], i.e. TA is expressed as TA=(AV−V∗0)where V is an isometry and A is an arbitrary linear operator, then we also investigate the local spectral properties of TA. As an application of these results, we discuss the existence of nontrivial invariant subspaces for such operators.
Fields of Study & Subjects
Holomorphic and Operator Theory
Advanced Topics in Algebra
Matrix Theory and Algorithms
Publication details
- Journal / source
- Linear and Multilinear Algebra
- Volume
- 74
- Issue
- 2
- Pages
- 166–181
- Publication date
- 2 January 2026
- Language
- EN