Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-08T08:37:08.449Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)