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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Uniqueness of the uniform norm with an application to topological algebras
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by S. J. Bhatt and D. J. Karia PDF
Proc. Amer. Math. Soc. 116 (1992), 499-503 Request permission

Abstract:

Any square-preserving linear seminorm on a unital commutative algebra is submultiplicative; and the uniform norm on a uniform Banach algebra is the only uniform $Q$-algebra norm on it. This is proved and is used to show that (i) uniform norm on a regular uniform Banach algebra is unique among all uniform (not necessarily complete) norms and (ii) a complete uniform topological algebra that is a $Q$-algebra is a uniform Banach algebra. Relevant examples, showing that the respective assumptions regarding regularity, $Q$-algebra norm, and uniform property of topology cannot be omitted, have been discussed.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 116 (1992), 499-503
  • MSC: Primary 46H05; Secondary 46J05
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1097335-4
  • MathSciNet review: 1097335