AN EXTENSION OF THE FUGLEDGE-PUTNAM THEOREM TO $\omega$-HYPONORMAL OPERATORS

The Fuglede-Putnam Theorem is that if A and B are normal operators and X is an operator such that AX = XB, then $A^{\ast}= X. In this paper, we show that if A is $\omega$-hyponormal and $B^{\ast}$ is invertible $\omega$-hyponormal such that AX = XB for a Hilbert-Schmidt operator X, then $A^{\ast}X = XB^{\ast}$.