Fuglede-Putnam Theorem for $w$-hyponormal or class $\mathcal{Y}$ operators

Abstract

‎An asymmetric Fuglede-Putnam's Theorem for $w$-hyponormal operators and class $\mathcal{Y}$ operators is proved‎, ‎as a consequence of this result‎, ‎we obtain that the range of the generalized derivation induced by the above classes of‎ ‎operators is orthogonal to its kernel‎.