Local spectral properties on skew diagonal operator matrices

Abstract

Let (Formula presented.) be similar to (Formula presented.) via an involution U. In this paper, we study the local spectral properties of T. Furthermore, if the operator (Formula presented.) 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. (Formula presented.) is expressed as (Formula presented.) where V is an isometry and A is an arbitrary linear operator, then we also investigate the local spectral properties of (Formula presented.) As an application of these results, we discuss the existence of nontrivial invariant subspaces for such operators. © 2026 Informa UK Limited, trading as Taylor & Francis Group.