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Some properties of the Pisier algebra

Published online by Cambridge University Press:  01 March 2000

THOMAS VILS PEDERSEN
THOMAS VILS PEDERSEN
Affiliation:
Laboratoire de Mathématiques Pures, Université Bordeaux 1 351, cours de la Libération, F-33405 Talence cédex, France; e-mail: vils@math.u-bordeaux.fr
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Abstract

The Pisier algebra [Pscr] consists of those continuous functions f on the unit circle [] for which

formula here

is continuous on [] almost surely, that is, for almost every choice of a sequence of signs (±1, ±1, …). In this paper, we prove that spectral synthesis holds in [Pscr]. Moreover, we show that certain closed ideals in [Pscr] with infinite hull have bounded approximate identities and give an example of a closed ideal in [Pscr] which does not have a bounded approximate identity.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 128 , Issue 2 , March 2000 , pp. 343 - 354
Copyright
© The Cambridge Philosophical Society 2000

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