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The Berberian's transform and an asymmetric Putnam-Fuglede theorem
Published 19 May 2014 in math.FA and math.OA | (1405.4844v3)
Abstract: We present how to apply a Berberian's technique to asymmetric Putnam-Fuglede theorems. In particular, we proved that if $A, B \in B(H)$ belong to the union of classes of $$-paranormal operators, p-hyponormal operators, dominant operators and operators of class Y and $AX = XB^$ for some $X \in B(H)$, then $A*X = XB$. Moreover, we gave a new counterexample for an asymmetric Putnam-Fuglede theorem for paranormal operators
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