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 Hilbert space H and $$T\in L(H)$$ T ? L ( H ) . We also the relationship between quasi-nilpotent part adjoint $$T^*$$ ? analytic core K ( T ) in case decomposable complex symmetric operators. last consider Weyl type theorems for triangular operator matrices which one entries has or $$JT^*J$$ J The theory exemplified concrete cases.