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Representation of a quotient of a subalgebra of B(X)

Published online by Cambridge University Press:  24 October 2008

Christian Le Merdy
Christian Le Merdy
Affiliation:
Equipe de Mathématiques, UA CNRS 741, Université de Franche-Comté, 25030 Besançon Cedex, France
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Abstract

Let X be an SQp-space, i.e. a quotient of a subspace of some Lp-space. Let B ⊂ B(X) be a subalgebra of all bounded operators on X and let I ⊂ B be a closed ideal. We show that the quotient algebra B/I is isometrically homomorphic to a subalgebra of B(Y) for some SQp-space Y. This generalizes a theorem of Bernard and Cole, corresponding to p = 2, which states that any quotient of an operator algebra is an operator algebra.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 1 , January 1996 , pp. 83 - 90
Copyright
Copyright © Cambridge Philosophical Society 1996

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