The spectral radius of a direct integral of operators
Author:
T. R. Chow
Journal:
Proc. Amer. Math. Soc. 26 (1970), 593-597
MSC:
Primary 47.30
DOI:
https://doi.org/10.1090/S0002-9939-1970-0283603-8
MathSciNet review:
0283603
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Abstract | References | Similar Articles | Additional Information
Abstract: The purpose of this paper is to give a formula for computing the spectral radius of a direct integral of operators from the numerical radius of its integrand. The direct sum of operators is a special case of our theorem. An example is given where our theorem cannot be applied.
- Jacques Dixmier, Les algèbres d’opérateurs dans l’espace hilbertien (Algèbres de von Neumann), Cahiers Scientifiques, Fasc. XXV, Gauthier-Villars, Paris, 1957 (French). MR 0094722
- Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
- J. T. Schwartz, $W^{\ast } $-algebras, Gordon and Breach Science Publishers, New York-London-Paris, 1967. MR 0232221
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Keywords:
Spectral radius,
numerical radius,
direct integral of operators,
unilateral weighted shift,
nilpotent,
quasi-nilpotent
Article copyright:
© Copyright 1970
American Mathematical Society