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# Character Amenability of the Intersection of Lipschitz Algebras

Published:2017-09-04
Printed: Dec 2017
• Fatemeh Abtahi,
Department of Mathematics, University of Isfahan, Isfahan, Iran
• Mohsen Azizi,
Department of Mathematics, University of Isfahan, Isfahan, Iran
• Ali Rejali,
Department of Mathematics, University of Isfahan, Isfahan, Iran
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## Abstract

Let $(X,d)$ be a metric space and $J\subseteq [0,\infty)$ be nonempty. We study the structure of the arbitrary intersections of Lipschitz algebras, and define a special Banach subalgebra of $\bigcap_{\gamma\in J}\operatorname{Lip}_\gamma X$, denoted by $\operatorname{ILip}_J X$. Mainly, we investigate $C$-character amenability of $\operatorname{ILip}_J X$, 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 $\operatorname{ILip}_J X$, specially Lipschitz algebras, under an additional assumption.
 Keywords: amenability, character amenability, Lipschitz algebra, metric space
 MSC Classifications: 46H05 - General theory of topological algebras 46J10 - Banach algebras of continuous functions, function algebras [See also 46E25] 11J83 - Metric theory

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