An extension of the Fuglede-Putnam theorem to subnormal operators using a Hilbert-Schmidt norm inequality
نویسندگان
چکیده
منابع مشابه
An Asymmetric Putnam–fuglede Theorem for Unbounded Operators
The intertwining relations between cosubnormal and closed hyponormal (resp. cohyponormal and closed subnormal) operators are studied. In particular, an asymmetric Putnam–Fuglede theorem for unbounded operators is proved.
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An operator T ∈ B(H) is called quasi-class (A, k) if T ∗k(|T | − |T |)T k ≥ 0 for a positive integer k, which is a common generalization of class A. The famous Fuglede–Putnam’s theorem is as follows: the operator equation AX = XB implies A∗X = XB∗ when A and B are normal operators. In this paper, firstly we show that if X is a Hilbert-Schmidt operator, A is a quasi-class (A, k) operator and B∗ ...
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We prove the following statements about bounded linear operators on a separable, complex Hilbert space: (1) Every normal operator N that is similar to a Hilbert-Schmidt perturbation of a diagonal operator D is unitarily equivalent to a Hilbert-Schmidt perturbation of D; (2) For every normal operator A', diagonal operator D and bounded operator X, the Hilbert-Schmidt norms (finite or infinite) o...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1981
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1981-0593465-4