Class $wA(s,t)$ operators and quasisimilarity

Abstract

In this paper it is shown that the normal parts of quasisimilar $wA(s,t)$ operators with $s+t=1$ are unitarily equivalent. Also, we establish the orthogonality of the range and the kernel of a nonnormal derivation with respect to the unitarily invariant norms associated with norm ideals of operators. Moreover, we obtain that the range of the generalized derivation induced by an pair satisfies Fuglede–Putnam property is orthogonal to its kernel.