Uniqueness of the uniform norm with an application to Topological Algebras

Bhatt, S. J. ; Karia, D. J. (1992) Uniqueness of the uniform norm with an application to Topological Algebras Proceedings of the American Mathematical Society, 116 (2). pp. 499-503. ISSN 0002-9939

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Official URL: http://www.ams.org/journals/proc/1992-116-02/S0002...

Related URL: http://dx.doi.org/10.1090/S0002-9939-1992-1097335-4

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.

Item Type:Article
Source:Copyright of this article belongs to American Mathematical Society.
Keywords:Uniform Banach Algebra; Regular Banach Algebra; Topological Algebra; Q-algebra
ID Code:59667
Deposited On:07 Sep 2011 04:47
Last Modified:18 May 2016 10:08

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