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ARE ALL UNIFORM ALGEBRAS AMNM?

Published online by Cambridge University Press:  01 May 1997

STUART J. SIDNEY
STUART J. SIDNEY
Affiliation:
Institut Fourier, URA 188 du CNRS, Université de Grenoble I, BP 74, 38402 St Martin d'He'res Cedex, France; Department of Mathematics, Box U-9, The University of Connecticut, Storrs, CT 06269-3009, USA
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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.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 3 , May 1997 , pp. 327 - 330
Copyright
© The London Mathematical Society 1997

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