Normality can be relaxed in the asymptotic Fuglede-Putnam theorem

Abstract

The original form of the Fuglede-Putnam theorem states that the operator equation A X = X B AX = XB implies A ∗ X = X B ∗ {A^ \ast }X = X{B^ \ast } when A and B are normal. In our previous paper we have relaxed the normality in the hypotheses on A and B as follows: if A and B ∗ {B^ \ast } are subnormal and if X is an operator such that A X = X B AX = XB , then A ∗ X = X B ∗ {A^ \ast }X = X{B^ \ast } . We shall show asymptotic versions of this generalized Fuglede-Putnam theorem; these results are also extensions of results of Moore and Rogers.