We consider k-quasi-M-hyponormal operators T ∈ B(ℋ) such that TX = XS for some X ∈ \( B\left(\mathcal{K},\mathrm{\mathscr{H}}\right) \) and prove a Fuglede–Putnam-type theorem when the adjoint of S ∈ \( B\left(\mathcal{K}\right) \) is either a k-quasi-M-hyponormal or a dominant operator. We also show that two quasisimilar k-quasi-M-hyponormal operators have identical essential spectra.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 1, pp. 89–98, January, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i1.2355.
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Mecheri, S., Prasad, T. Fuglede–Putnam-Type Theorems for the Extensions of M-Hyponormal Operators. Ukr Math J 74, 102–113 (2022). https://doi.org/10.1007/s11253-022-02050-0
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DOI: https://doi.org/10.1007/s11253-022-02050-0