Fuglede – Putnam type theorems for extension of $M$-hyponormal operators - Mecheri , S.; Prasad , T. (Ukrains’kyi Matematychnyi Zhurnal, 2022)
UDC 517.9We consider $k$-quasi-$M$-hyponormal operator $T \in B(\mathcal{H})$ suchthat $TX = XS$ 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.