## African Diaspora Journal of Mathematics

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

M. H. M. Rashid

#### 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.

#### Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 14, Number 1 (2012), 106-118.

Dates
First available in Project Euclid: 18 July 2013

Mathematical Reviews number (MathSciNet)
MR3080400

Zentralblatt MATH identifier
06227069

Subjects
Primary: 47B20; 47A10; 47A11

#### Citation

Rashid, M. H. M. An Extension of Fuglede-Putnam Theorem for $w$-Hyponormal Operators. Afr. Diaspora J. Math. (N.S.) 14 (2012), no. 1, 106--118. https://projecteuclid.org/euclid.adjm/1374153559

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