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december 2010 Criteria of existence of bounded approximate identities in topological algebras
Christina P. Podara
Bull. Belg. Math. Soc. Simon Stevin 17(5): 949-960 (december 2010). DOI: 10.36045/bbms/1292334069

Abstract

Some results and criteria of existence concerning bounded approximate identities in Banach algebras are extended to the topological algebras setting. We thereby prove that the bidual of a commutative locally C*-algebra with either of the two Arens products is a unital commutative algebra, and that a quasinormable Fréchet m-convex algebra has a left (resp. right) bounded approximate identity if and only if it can be represented as an inverse limit of Banach algebras each of which has a left (resp. right) bounded approximate identity.

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Christina P. Podara. "Criteria of existence of bounded approximate identities in topological algebras." Bull. Belg. Math. Soc. Simon Stevin 17 (5) 949 - 960, december 2010. https://doi.org/10.36045/bbms/1292334069

Information

Published: december 2010
First available in Project Euclid: 14 December 2010

zbMATH: 1214.46029
MathSciNet: MR2777784
Digital Object Identifier: 10.36045/bbms/1292334069

Subjects:
Primary: 46H20
Secondary: 46A20 , 46H25 , 46K05 , 46M18 , 46M40

Keywords: Approximate identity/units , Arens products , Arens regularity , bidual of a locally convex algebra , quasinormable Fréchet m-convex algebra , Topological algebra

Rights: Copyright © 2010 The Belgian Mathematical Society

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Vol.17 • No. 5 • december 2010
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