Fuglede-Putnam Type Theorems Via the Moore-Penrose Inverse and Aluthge Transform

Let a, b ∈ b(h), where h is a hilbert space. let t and t† denote the aluthge transform and the moore-penrose inverse of t, respectively. we show that (i) if a∗ is quasinormal, then ((a) †, (b) †) has the f p-property; (ii) if (a†, b†) has the f p-property, then so has ((a) †, (b) †). in general, (t) † = t †. finally, we give some applications to the lambert multiplication operator mwemu on l^2(σ), where e is the conditional expectation operator.