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arXiv · 1405.4844

The Berberian's transform and an asymmetric Putnam-Fuglede theorem

Ahmed Bachir·Patryk Pagacz
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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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Ahmed Bachir, Patryk Pagacz. 2014-05-19. The Berberian's transform and an asymmetric Putnam-Fuglede theorem. https://doi.org/10.1007/s11785-022-01233-8

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