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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.


References [Enhancements On Off] (What's this?)

  • 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 $H^\infty$ 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

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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

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