Property $(U{W}_E)$ and Consistent invertibility

Abstract

In this paper, we study the stability of Property $(U{W}_E)$ under commuting finite rank perturbation in terms of spectrum induced by consistent in invertibility for operators and a variant of upper semi-Weyl spectrum. Also we discuss the stability of Property $(U{W}_E)$ under direct sum $T\oplus S$ and tensor product $T\otimes S$ for Hilbert space operators $T$ and $S$.