Fuglede – Putnam type theorems for extension of $M$-hyponormal operators

Keywords: Fuglede-Putnam theorem, normal operator, k-quasi-M-hyponormal operator, dominant operator, and quasisimilar 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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Published
24.01.2022
How to Cite
Mecheri , S., and T. Prasad. “Fuglede – Putnam Type Theorems for Extension of $M$-Hyponormal Operators”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 1, Jan. 2022, pp. 89 - 98, doi:10.37863/umzh.v74i1.2355.
Section
Research articles