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ARE ALL UNIFORM ALGEBRAS AMNM?
Published online by Cambridge University Press: 01 May 1997
Abstract
A Banach algebra [afr ] is AMNM if whenever a linear functional ϕ on [afr ] and a positive number δ satisfy [mid ]ϕ(ab)−ϕ(a)ϕ(b)[mid ] [les ]δ|a|·|b| for all a, b∈[afr ], there is a multiplicative linear functional ψ on [afr ] such that |ϕ−ψ|=o(1) as δ→0. K. Jarosz [1] asked whether every Banach algebra, or every uniform algebra, is AMNM. B. E. Johnson [3] studied the AMNM property and constructed a commutative semisimple Banach algebra that is not AMNM. In this note we construct uniform algebras that are not AMNM.
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- Research Article
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- © The London Mathematical Society 1997
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