Local Spectral Properties Under Conjugations

Abstract

In this paper, we study some local spectral properties of operators having form JTJ, where J is a conjugation on a Hilbert space H and T∈ L(H). We also study the relationship between the quasi-nilpotent part of the adjoint T∗ and the analytic core K(T) in the case of decomposable complex symmetric operators. In the last part we consider Weyl type theorems for triangular operator matrices for which one of the entries has form JTJ, or has form JT∗J. The theory is exemplified in some concrete cases.