The Fuglede-Putnam Theorem and Quasinormality for Class p-wA(s, t) Operators

Abstract

In this work, we demonstrate that (i) if T is a class p-wA(s, t) operator and T(s, t) is quasinormal (resp., normal), then T is also quasinormal (resp., normal) (ii) If T and T∗ are class p-wA(s, t) operators, then T is normal; (iii) the normal portions of quasisimilar class p-wA(s, t) operators are unitarily equivalent; and (iv) Fuglede-Putnam type theorem holds for a class p-wA(s, t) operator T for 0< s, t, s + t = 1 and 0 < p ≤ 1 if T satisfies a kernel condition ker(T) ⊂ ker(T∗).