An Extension of Fuglede-Putnam Theorem for $w$-HyponormalOperators

Abstract

In this paper, we prove the following: assume that either (i) $T^*$ is $w$-hyponormal and $S$ is $w$-hyponormal such that $\ker(T^*)\subset\ker(T)$ and $\ker(S)\subset\ker(S^*)$ or (ii) $T^*$ is $p$-hyponormal or $\log$-hyponormal and $S$ is $w$-hyponormal such that $\ker(S)\subset\ker(S^*)$ or (iii) $T^*$ is an injective $w$-hyponormal and $S$ is a dominant holds. Then the pair $(T,S)$ satisfy Fuglede-Putnam theorem. Also, other related results are given.