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

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

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

Email:
tfeeman@email.vill.edu

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

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