On higher order Bourgain algebras of a nest algebra

Feeman, Timothy

doi:10.1090/S0002-9939-98-04329-9

On higher order Bourgain algebras of a nest algebra
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by Timothy G. Feeman

Proc. Amer. Math. Soc. 126 (1998), 1391-1396

DOI: https://doi.org/10.1090/S0002-9939-98-04329-9

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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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