Extensions of a theorem of Fuglede and Putnam
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- by S. K. Berberian PDF
- Proc. Amer. Math. Soc. 71 (1978), 113-114 Request permission
Abstract:
The operator equation $AX = XB$ implies ${A^ \ast }X = X{B^ \ast }$ when A and B are normal (theorem of Fuglede and Putnam). If X is of Hilbert-Schmidt class, the assumptions on A and B can be relaxed: it suffices that A and ${B^ \ast }$ be hyponormal, or that B be invertible with $\left \| A \right \|\left \| {{B^{ - 1}}} \right \| \leqslant 1$.References
- S. K. Berberian, Note on a theorem of Fuglede and Putnam, Proc. Amer. Math. Soc. 10 (1959), 175–182. MR 107826, DOI 10.1090/S0002-9939-1959-0107826-9 —, Introduction to Hilbert space, Chelsea, New York, 1976. J. Dixmier, Les algèbres d’opérateurs dans l’espace hilbertien (Algèbres de von Neumann), 2nd ed., Gauthier-Villars, Paris, 1969.
- Paul Richard Halmos, A Hilbert space problem book, 2nd ed., Encyclopedia of Mathematics and its Applications, vol. 17, Springer-Verlag, New York-Berlin, 1982. MR 675952 F. Riesz and B. Sz.-Nagy, Leçons d’analyse fonctionelle, Akadémia Kiadó, Budapest, 1952.
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 71 (1978), 113-114
- MSC: Primary 47B20; Secondary 47B10
- DOI: https://doi.org/10.1090/S0002-9939-1978-0487554-2
- MathSciNet review: 0487554