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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Banach algebras with unique uniform norm
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by S. J. Bhatt and H. V. Dedania PDF
Proc. Amer. Math. Soc. 124 (1996), 579-584 Request permission

Abstract:

Commutative semisimple Banach algebras that admit exactly one uniform norm (not necessarily complete) are investigated. This unique uniform norm property is completely characterized in terms of each of spectral radius, Silov boundary, set of uniqueness, semisimple norms; and its connection with recently investigated concepts like spectral extension property, multiplicative Hahn Banach extension property and permanent radius are revealed. Several classes of Banach algebras having this property as well as those not having this property are discussed.
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Additional Information
  • S. J. Bhatt
  • Affiliation: Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388 120, Gujarat, India
  • H. V. Dedania
  • Affiliation: Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388 120, Gujarat, India
  • Address at time of publication: Department of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
  • MR Author ID: 338194
  • ORCID: 0000-0002-6353-6924
  • Received by editor(s): May 16, 1994
  • Received by editor(s) in revised form: September 12, 1994
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 579-584
  • MSC (1991): Primary 46J05
  • DOI: https://doi.org/10.1090/S0002-9939-96-03063-8
  • MathSciNet review: 1301488