On higher order Bourgain algebras of a nest algebra
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- by Timothy G. Feeman PDF
- Proc. Amer. Math. Soc. 126 (1998), 1391-1396 Request permission
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
- J. Bourgain, The Dunford-Pettis property for the ball-algebras, the polydisc-algebras and the Sobolev spaces, Studia Math. 77 (1984), no. 3, 245–253. MR 745280, DOI 10.4064/sm-77-3-246-253
- Joseph A. Cima and Richard M. Timoney, The Dunford-Pettis property for certain planar uniform algebras, Michigan Math. J. 34 (1987), no. 1, 99–104. MR 873024, DOI 10.1307/mmj/1029003487
- Joseph A. Cima, Svante Janson, and Keith Yale, Completely continuous Hankel operators on $H^\infty$ and Bourgain algebras, Proc. Amer. Math. Soc. 105 (1989), no. 1, 121–125. MR 931727, DOI 10.1090/S0002-9939-1989-0931727-6
- Kenneth R. Davidson, Nest algebras, Pitman Research Notes in Mathematics Series, vol. 191, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1988. Triangular forms for operator algebras on Hilbert space. MR 972978
- Timothy G. Feeman, Nest algebras of operators and the Dunford-Pettis property, Canad. Math. Bull. 34 (1991), no. 2, 208–214. MR 1113298, DOI 10.4153/CMB-1991-033-7
- T. G. Feeman, The Bourgain algebra of a nest algebra, Proc. Edinburgh Math. Soc. (2), 40 (1997), 151–166.
- Pamela Gorkin, Keiji Izuchi, and Raymond Mortini, Bourgain algebras of Douglas algebras, Canad. J. Math. 44 (1992), no. 4, 797–804. MR 1178569, DOI 10.4153/CJM-1992-047-6
- Keiji Izuchi, Karel Stroethoff, and Keith Yale, Bourgain algebras of spaces of harmonic functions, Michigan Math. J. 41 (1994), no. 2, 309–321. MR 1278437, DOI 10.1307/mmj/1029004998
Additional Information
- Timothy G. Feeman
- Affiliation: Department of Mathematical Sciences, Villanova University, Villanova, Pennsylvania 19085
- Email: tfeeman@email.vill.edu
- Received by editor(s): October 14, 1996
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- 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