Fuglede–Putnam type theorems for ( p , k ) $(p,k)$ -quasihyponormal operators via hyponormal operators

For Hilbert space operators S, X, and T, \((S,X,T)\in FP\) means Fuglede–Putnam theorem holds for triplet \((S,X,T)\), that is, \(SX=XT\) ensures \(S^{\ast }X=XT^{\ast }\). Similarly, \((S,T)\in FP\) means \((S,X,T)\in FP\) holds for each operator X. This paper is devoted to the study of Fuglede–Putnam type theorems for \((p,k)\)-quasihyponormal operators via a class of operators based on hyponormal operators \(FP(H):=\{S|(S,T)\in FP \mbox{ holds for each hyponormal operator } T^{\ast }\}\). Fuglede–Putnam type theorems involving \((p,k)\)-quasihyponormal, dominant, and w-hyponormal operators, which are extensions of the results by Tanahashi, Patel, Uchiyama, et al., are obtained.