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Character Amenability of the Intersection of Lipschitz Algebras

Published online by Cambridge University Press:  20 November 2018

Fatemeh Abtahi ,
Mohsen Azizi  and
Ali Rejali
Fatemeh Abtahi
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan, Iran e-mail: f.abtahi@sci.ui.ac.irm.azizi@sci.ui.ac.irrejali@sci.ui.ac.ir
Mohsen Azizi
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan, Iran e-mail: f.abtahi@sci.ui.ac.irm.azizi@sci.ui.ac.irrejali@sci.ui.ac.ir
Ali Rejali
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan, Iran e-mail: f.abtahi@sci.ui.ac.irm.azizi@sci.ui.ac.irrejali@sci.ui.ac.ir
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Abstract

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Let $(X,d)$ be a metric space and let $J\subseteq [0,\infty )$ be nonempty. We study the structure of the arbitrary intersections of Lipschitz algebras and define a special Banach subalgebra of ${{\cap }_{\gamma \in J\,}}\text{Li}{{\text{p}}_{\gamma \,}}X$, denoted by $\text{ILi}{{\text{p}}_{J}}X$. Mainly, we investigate the $C$-character amenability of $\text{ILi}{{\text{p}}_{J}}X$, in particular Lipschitz algebras. We address a gap in the proof of a recent result in this field. Then we remove this gap and obtain a necessary and sufficient condition for $C$-character amenability of $\text{ILi}{{\text{p}}_{J}}X$, specially Lipschitz algebras, under an additional assumption.

Keywords

46H05046J1011J83amenabilitycharacter amenabilityLipschitz algebrametric space
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 4 , 01 December 2017 , pp. 673 - 689
Copyright
Copyright © Canadian Mathematical Society 2017

References

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