FUGLEDE-PUTNAM-TYPE THEOREMS FOR THE EXTENSIONS OF M-HYPONORMAL OPERATORS

摘要

We consider k-quasi-M-hyponormal operators T is an element of B(H) such that TX= XS for some X is an element of B(K, H) and prove a Fuglede-Putnam-type theorem when the adjoint of S is an element of B(K) 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.