Fuglede – Putnam type theorems for extension of $M$-hyponormal operators
Abstract
UDC 517.9
We consider $k$-quasi-$M$-hyponormal operator $T \in B(\mathcal{H})$ such
that $TX = XS$ for some $X \in B(\mathcal{K},\mathcal{H})$ and prove the Fuglede–Putnam type theorem when adjoint of $S \in B(\mathcal{K})$ is $k$-quasi-$M$-hyponormal or dominant operators.
We also show that two quasisimilar $k$-quasi-$M$-hyponormal operators have equal essential spectra.
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