Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2019; 34(2): 585-602

Online first article March 5, 2019      Printed April 1, 2019

https://doi.org/10.4134/CKMS.c180209

Copyright © The Korean Mathematical Society.

Algebras of Gelfand-continuous functions into Arens-Michael algebras

Lahbib Oubbi

University Mohammed V in Rabat

Abstract

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We characterize Gelfand-continuous functions from a Tychonoff space $X$ into an Arens-Michael algebra $A$. Then we define several algebras of such functions, and investigate them as topological algebras. Finally, we provide a class of examples of (metrizable) commutative unital complete Arens-Michael algebras $A$ and locally compact spaces $X$ for which all these algebras differ from each other.

Keywords: Gelfand-continuous function, Arens-Michael algebra, locally multiplicatively convex algebra, character, Gelfand representation

MSC numbers: Primary 46J05, 46J10, 46H05, 46E25

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