On generalized Fuglede-Putnam theorems of Hilbert-Schmidt type
نویسندگان
چکیده
منابع مشابه
On the Putnam-Fuglede theorem
We extend the Putnam-Fuglede theorem and the second-degree Putnam-Fuglede theorem to the nonnormal operators and to an elementary operator under perturbation by quasinilpo-tents. Some asymptotic results are also given.
متن کاملNote on a Theorem of Fuglede and Putnam
1. An involution in a ring A is a mapping a—^a* (a(Ei;A) such that a**=a, (a+b)*=a*+b*, (ab)* = b*a*. An element a&A is (1) normal if a*a=aa*, (2) self-adjoint if a*=a, (3) unitary if a*a=aa* = l (1= unity element of A). We say that "Fuglede's theorem holds in A" incase the relations a(E.A, a normal, b^A, ba=ab, imply ba* = a*b; briefly, A is an FT-ring. It follows from a theorem of B. Fuglede ...
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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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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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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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1983
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1983-0695261-8