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The Operator Amenability of Uniform Algebras

  Published:2003-12-01
 Printed: Dec 2003
  • Volker Runde
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Abstract

We prove a quantized version of a theorem by M.~V.~She\u{\i}nberg: A uniform algebra equipped with its canonical, {\it i.e.}, minimal, operator space structure is operator amenable if and only if it is a commutative $C^\ast$-algebra.
Keywords: uniform algebras, amenable Banach algebras, operator amenability, minimal, operator space uniform algebras, amenable Banach algebras, operator amenability, minimal, operator space
MSC Classifications: 46H20, 46H25, 46J10, 46J40, 47L25 show english descriptions Structure, classification of topological algebras
Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
Banach algebras of continuous functions, function algebras [See also 46E25]
Structure, classification of commutative topological algebras
Operator spaces (= matricially normed spaces) [See also 46L07]
46H20 - Structure, classification of topological algebras
46H25 - Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46J10 - Banach algebras of continuous functions, function algebras [See also 46E25]
46J40 - Structure, classification of commutative topological algebras
47L25 - Operator spaces (= matricially normed spaces) [See also 46L07]
 

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