Fuglede's theorem
Theorem (Fuglede) Let T and N be bounded operators on a complex Hilbert space with N being normal. If TN = NT, then TN* = N*T, where N* denotes the adjoint of N. Normality of N is necessary, as is seen by taking T=N. When T is self-adjoint, the claim is trivial regardless of whether N is normal: Tentative Proof: … See more In mathematics, Fuglede's theorem is a result in operator theory, named after Bent Fuglede. See more The theorem can be rephrased as a statement about elements of C*-algebras. Theorem (Fuglede-Putnam-Rosenblum) Let x, y be two … See more The following contains Fuglede's result as a special case. The proof by Rosenblum pictured below is just that presented by Fuglede for his … See more WebJul 5, 2024 · Fuglede’s theorem August 2015 License CC BY-NC-SA Authors: V.S. Sunder Abstract In this short note, we give an elementary (set-theoretic) proof of Fuglede’s …
Fuglede's theorem
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Webmodulus of a system of measures in the sense of Fuglede [7]. The following result is a consequence of Theorem 5.5 and shows that even sets of zero measure can have the property of having minimal products, provided they are minimal themselves. Theorem 1.2. If EˆR is minimal and supports a measure s.t. for every ">0 (1.2) r1+". (E\B r(x)) .r1 " WebThe result. Theorem (Fuglede) Let T and N be bounded operators on a complex Hilbert space with N being normal. If TN = NT, then TN* = N*T, where N* denotes the adjoint of N . Normality of N is necessary, as is seen by taking T = N. When T is self-adjoint, the claim is trivial regardless of whether N is normal: T N ∗ = ( N T) ∗ = ( T N) ∗ ...
WebIntroduction Undoubtedly, the Fuglede Theorem is the second salient result in Operator The- ory, at least, as far as normal operators are concerned. It has many applications. … WebJan 26, 2024 · The Fuglede Theorem and Some Intertwining Relations. Ikram Fatima Zohra Bensaid, Souheyb Dehimi, Bent Fuglede, Mohammed Hichem Mortad. In this paper, we …
WebThe familiar Fuglede-Putnam theorem is as follows ([3, Problem 152], [4]). Theorem A. If A and B are normal operators and if X is an operator such that AX = XB, then A*X = XB*. In this paper we relax the normality in the hypotheses on A and B in Theorem A, namely, we show that the normality can be replaced by the WebThis theorem has been generalized [13, 7] as follows. THEOREM A. Let A, B, and X be operators on H, where A and B* are subnormal. Then AX = XB implies A*X = XB*. In a series of papers [12-14], G. Weiss considered the Fuglede-Putnam theorem modulo certain operator ideals, and his work culminates in the following remarkable result. THEOREM B.
WebAug 17, 2024 · In particular, an asymmetric Putnam–Fuglede theorem for unbounded operators is proved. View. Show abstract. An application of the Putnam-Fuglede …
WebApr 17, 2009 · At first we investigate the similarity between the Kleinecke-Shirokov theorem for subnormal operators and the Fuglede-Putnam theorem and also we show an asymptotic version of this similarity. These results generalize results of Ackermans, van Eijndhoven and Martens. Also we show two theorems on degree of approximation on … lingam significationWeboperators in Hilbert space which is an extension of Fuglede's theorem. It states in essence that if N is a normal operator and A a densely defined linear operator which has a closure (i.e., A* is densely defined), D(N)cD(A*), and NAx=ANx for an appropriate set of vectors x (cf. Theorem 1), then the spectral measure of N permutes with A. lingam steam herbsWeband C, is the trace class. The Fuglede-Putnam theorem states that if N and M are normal operators in B(H) and NX = XM for some X E B(H), then N*X = XM*. This theorem has … lingam steaming herbs for menWebOct 16, 2024 · The Fuglede theorem plays a prominent role in the study of normal operators. Probably the main application of this theorem is the fact that it improves … hot tub repair walla wallaWebJul 1, 2024 · Fuglede–Putnam theorems, Berberian–Putnam–Fuglede theorems. Let $H$ denote a Hilbert space, $B ( H )$ the algebra of operators on $H$ (i.e., bounded linear … lingam therapyhot tub repair waupaca wiWebFeb 28, 2024 · As immediate applications of the Fuglede theorem, we have: Theorem 12.1.3. Let A, B ∈ B(H) be both normal and such that AB = BA. Then (1) AB, A ∗ B ∗, AB … hot tub repair traverse city mi