On extensions of some Flugede-Putnam type theorems involving (p, k)-quasihyponormal, spectral, and dominant operators

A Hilbert space operator S is called (p, k)-quasihyponormal if S *k((S *S)p – (SS *)p)Sk ≥ 0 for an integer k ≥ 1 and 0 < p ≤ 1. In the present note, we consider (p, k)-quasihyponormal operator S ∈ B (H) such that SX = XT for some X ∈ B (K,H) and prove the Fuglede–Putnam type theorems when the adjoint of T ∈ B (K) is either (p, k)-quasihyponormal or dominant or a spectral operator (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)