The Fuglede-Putnam theorem and Putnam’s inequality for quasi-class (A, k) operators. (English) Zbl 1219.47036
Summary: An operator is called quasi-class if for a positive integer , which is a common generalization of class A. The famous Fuglede-Putnam theorem is as follows: the operator equation implies when and are normal operators. In this paper, firstly we show that, if is a Hilbert-Schmidt operator, is a quasi-class operator and is an invertible class A operator such that , then . Secondly, we consider Putnam’s inequality for quasi-class operators and we also show that quasisimilar quasi-class operators have equal spectrum and essential spectrum.
|47B20||Subnormal operators, hyponormal operators, etc.|