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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On higher order Bourgain algebras
of a nest algebra

Author: Timothy G. Feeman
Journal: Proc. Amer. Math. Soc. 126 (1998), 1391-1396
MSC (1991): Primary 47D25
MathSciNet review: 1451799
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Abstract: Following earlier work in which we provided algebraic characterizations of the right, left, and two-sided Bourgain algebras, as well as the second order Bourgain algebras, associated with a nest algebra, we herein demonstrate that a given nest algebra has (essentially) at most six different third order Bourgain algebras, and that every fourth order (or higher) Bourgain algebra of the nest algebra coincides with one of at most third order. This puts the final touch on the description of Bourgain algebras of nest algebras.

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Additional Information

Timothy G. Feeman
Affiliation: Department of Mathematical Sciences, Villanova University, Villanova, Pennsylvania 19085

Keywords: Nest algebra, Bourgain algebra
Received by editor(s): October 14, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society