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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