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. 499503. ISSN 00029939

PDF
 Publisher Version
551kB 
Official URL: http://www.ams.org/journals/proc/199211602/S0002...
Related URL: http://dx.doi.org/10.1090/S00029939199210973354
Abstract
Any squarepreserving linear seminorm on a unital commutative algebra is submultiplicative; and the uniform norm on a uniform Banach algebra is the only uniform Qalgebra 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 Qalgebra is a uniform Banach algebra. Relevant examples, showing that the respective assumptions regarding regularity, Qalgebra 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; Qalgebra 
ID Code:  59667 
Deposited On:  07 Sep 2011 04:47 
Last Modified:  18 May 2016 10:08 
Repository Staff Only: item control page