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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
MathSciNet review: 0283603
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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.


References [Enhancements On Off] (What's this?)

  • [1] Jacques Dixmier, Les algèbres d’opérateurs dans l’espace hilbertien (Algèbres de von Neumann), Cahiers scientifiques, Fascicule XXV, Gauthier-Villars, Paris, 1957 (French). MR 0094722
  • [2] Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
  • [3] J. T. Schwartz, 𝑊*-algebras, Gordon and Breach Science Publishers, New York-London-Paris, 1967. MR 0232221

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0283603-8
Keywords: Spectral radius, numerical radius, direct integral of operators, unilateral weighted shift, nilpotent, quasi-nilpotent
Article copyright: © Copyright 1970 American Mathematical Society