Bull. Korean Math. Soc. 2006; 43(4): 747-753
Printed December 1, 2006
Copyright © The Korean Mathematical Society.
Salah Mecheri, K^{o}tar^{o} Tanahashi, and Atsushi Uchiyama
King Saud University, Tohoku Pharmaceutical University, Sendai National College of Technology
We say operators $A, B$ on Hilbert space satisfy Fuglede-Putnam theorem if $AX=XB$ for some $X$ implies $A^{*}X=XB^{*}$. We show that if either (1) $A$ is $p$-hyponormal and $B^{*}$ is a class $ {\mathcal Y}$ operator or (2) $A$ is a class $ {\mathcal Y}$ operator and $B^{*}$ is $p$-hyponormal, then $A, B$ satisfy Fuglede-Putnam theorem.
Keywords: $p$-hyponormal operator, class ${\mathcal Y}$, Fuglede-Putnam theo-rem
MSC numbers: 47B20
2002; 39(4): 527-534
2005; 42(3): 543-554
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