A Fuglede-Putnam theorem modulo the Hilbert-Schmidt class for almost normal operators with finite modulus of Hilbert-Schmidt quasi-triangularity

Abstract

We extend the Fuglede-Putnam theorem modulo the Hilbert-Schmidt class to almost normal operators with finite Hilbert-Schmidt modulus of quasi-triangularity.

Keywords

• Hilbert-Schmidt and trace-class operators
• Almost normal operators
• Almost hyponormal operators
• Modulus of quasi-triangularity