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The Bourgain algebra of a nest algebra

Published online by Cambridge University Press:  20 January 2009

Timothy G. Feeman
Timothy G. Feeman
Affiliation:
Department of Mathematical Sciences, Villanova University, Villanova, PA 19085, U.S.A.
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Abstract

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In analogy with a construction from function theory, we herein define right, left, and two-sided Bourgain algebras associated with an operator algebra A. These algebras are defined initially in Banach space terms, using the weak-* topology on A, and our main result is to give a completely algebraic characterization of them in the case where A is a nest algebra. Specifically, if A = alg N is a nest algebra, we show that each of the Bourgain algebras defined has the form A + K ∩ B, where B is the nest algebra corresponding to a certain subnest of N. We also characterize algebraically the second-order (and higher) Bourgain algebras of a nest algebra, showing for instance that the second-order two-sided Bourgain algebra coincides with the two-sided Bourgain algebra itself in this case.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 1 , February 1997 , pp. 151 - 166
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

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