Fuglede-Putnam theorem for locally measurable operators
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∗ ...
متن کاملPutnam-fuglede Theorem and the Range-kernel Orthogonality of Derivations
Let (H) denote the algebra of operators on a Hilbert space H into itself. Let d= δ or , where δAB : (H)→ (H) is the generalized derivation δAB(S)=AS−SB and AB : (H) → (H) is the elementary operator AB(S) = ASB−S. Given A,B,S ∈ (H), we say that the pair (A,B) has the property PF(d(S)) if dAB(S) = 0 implies dA∗B∗(S) = 0. This paper characterizes operators A,B, and S for which the pair (A,B) has p...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2017
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13845