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 WebDec 1, 2024 · V. L aurio and C. M. P earoy, Trace-class commutators with trace zero, Acta Sci. Math. (Szeged), 66 (2000), 341–349.. MathSciNet MATH Google Scholar . V. S hulman, Some remarks on the Fuglede-Weiss theorem, Bull. London Math. Soc., 28 (1996), 385–392. Article MathSciNet Google Scholar . V. S hulman and L. T urowska, Operator …
ON FUGLEDE’S CONJECTURE FOR THREE INTERVALS
WebMar 20, 2024 · Abstract. We review the definition of determinants for finite von Neumann algebras, due to Fuglede and Kadison [Fuglede B, Kadison R (1952) Ann Math 55:520–530], and a generalization for appropriate groups of invertible elements in Banach algebras, from a paper by Skandalis and the author (1984). After some discussion of K … WebMar 20, 2024 · Bent Fuglede is a Danish mathematician born in 1925. He has been working on mathematical analysis; he is also known for a book on Harmonic Maps Between … bbc jang
ON GENERALIZED FUGLEDE-PUTNAM THEOREMS OF …
WebMay 7, 2024 · Fuglede–Putnam type theorems involving (p,k) -quasihyponormal, dominant, and w -hyponormal operators, which are extensions of the results by Tanahashi, Patel, … WebA bounded linear operator N on a complex Hilbert space H is called normal in case NN* = N*N. One of the most useful results concerning normal operators is Fuglede's theorem [2], which states that any bounded linear operator B on H satisfying BN = NB also satisfies BN* = N*B. Moore [5], using techniques inspired by those of Rosenblum [6], proves an … 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) ∗ ... bbc jamaica inn part 9