Fuglede-Putnam theorem for $p$-hyponormal or class ${mathcal Y}$ operators

摘要

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.