Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1970-0283603-8
MathSciNet review: 0283603
Full-text PDF

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.


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

  • [1] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien (Algèbres de von Neumann), Cahiers Scientifiques, fasc. 25, Gauthier-Villars, Paris, 1957. MR 20 #1234. MR 0094722 (20:1234)
  • [2] P. Halmos, A Hilbert space problem book, Van Nostrand, Princeton, N.J., 1967. MR 34 #8178. MR 0208368 (34:8178)
  • [3] J. T. Schwartz, $ {W^ \ast }$-algebras, Gordon and Breach, New York, 1967. MR 38 #547. MR 0232221 (38:547)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47.30

Retrieve articles in all journals with MSC: 47.30


Additional Information

DOI: https://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

American Mathematical Society