|
On higher order Bourgain algebras of a nest algebra
Author(s):
Timothy
G.
Feeman
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1391-1396.
MSC (1991):
Primary 47D25
MathSciNet review:
1451799
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
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.
References:
- 1.
- J. Bourgain, The Dunford-Pettis property for the ball-algebras, the polydisc-algebras, and the Sobolev spaces, Studia Math., 77 (1984), 245-253. MR 85f:46044
- 2.
- J. A. Cima and R. M. Timoney, The Dunford-Pettis property for certain planar uniform algebras, Michigan Math. J., 34 (1987), 99-104. MR 88e:46023
- 3.
- J. A. Cima, S. Janson, and K. Yale, Completely continuous Hankel operators on
 and Bourgain algebras, Proc. Amer. Math. Soc., 105 (1989), 121-125. MR 89g:30065 - 4.
- K. R. Davidson, Nest Algebras, Pitman Research Notes in Mathematics, Vol. 191, Longman Scientific and Technical Pub. Co., London and New York, 1988. MR 90f:47062
- 5.
- T. G. Feeman, Nest algebras of operators and the Dunford-Pettis property, Canad. Math. Bull., 34 (1991), 208-214. MR 92e:47074
- 6.
- T. G. Feeman, The Bourgain algebra of a nest algebra, Proc. Edinburgh Math. Soc. (2), 40 (1997), 151-166. CMP 97:09
- 7.
- P. Gorkin, K. Izuchi, and R. Mortini, Bourgain algebras of Douglas algebras, Canad. J. Math., 44 (1992), 797-804. MR 94c:46104
- 8.
- K. Izuchi, K. Stroethoff, and K. Yale, Bourgain algebras of spaces of harmonic functions, Michigan Math. J., 41 (1994), 309-322. MR 95d:46051
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
47D25
Retrieve articles in all Journals with
MSC (1991):
47D25
Additional Information:
Timothy
G.
Feeman
Affiliation:
Department of Mathematical Sciences, Villanova University, Villanova, Pennsylvania 19085
Email:
tfeeman@email.vill.edu
DOI:
10.1090/S0002-9939-98-04329-9
PII:
S 0002-9939(98)04329-9
Keywords:
Nest algebra,
Bourgain algebra
Received by editor(s):
October 14, 1996
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1998,
American Mathematical Society
|
