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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Normality can be relaxed in the asymptotic Fuglede-Putnam theorem

Author: Takayuki Furuta
Journal: Proc. Amer. Math. Soc. 79 (1980), 593-596
MSC: Primary 47B20
MathSciNet review: 572310
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Abstract: The original form of the Fuglede-Putnam theorem states that the operator equation $ AX = XB$ implies $ {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^ \ast }$ are subnormal and if X is an operator such that $ AX = XB$, then $ {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.

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Keywords: Quasinormal operator, subnormal operator, hyponormal operator, operator topology
Article copyright: © Copyright 1980 American Mathematical Society