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An Extension of Fuglede-Putnam Theorem for w-Hyponormal Operators

Volume 14, Number 1 (2012), 106 - 118

An Extension of Fuglede-Putnam Theorem for w-Hyponormal Operators

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Abstract

In this paper, we prove the following: assume that either (i) $T^*$ is $w$-hyponormal and $S$ is $w$-hyponormal such that $n(T^*) \subset n(T)$ and $n(S)\subset n(S^*)$ or (ii) $T^*$ is $p$-hyponormal or $\log$-hyponormal and $S$ is $w$-hyponormal such that $n(S)\subset n(S^*)$ 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.