Extensions of a theorem of Fuglede and Putnam
Author:
S. K. Berberian
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
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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 $\left \| A \right \|\left \| {{B^{ - 1}}} \right \| \leqslant 1$.
- S. K. Berberian, Note on a theorem of Fuglede and Putnam, Proc. Amer. Math. Soc. 10 (1959), 175–182. MR 107826, DOI https://doi.org/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., Graduate Texts in Mathematics, vol. 19, Springer-Verlag, New York-Berlin, 1982. Encyclopedia of Mathematics and its Applications, 17. MR 675952 F. Riesz and B. Sz.-Nagy, Leçons d’analyse fonctionelle, Akadémia Kiadó, Budapest, 1952.
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Article copyright:
© Copyright 1978
American Mathematical Society
