$C(K,A)$ and $C(K,H^{\infty })$ have the Dunford-Pettis property
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- by Manuel D. Contreras and Santiago Díaz PDF
- Proc. Amer. Math. Soc. 124 (1996), 3413-3416 Request permission
Abstract:
Denote by $X$ either the disc algebra $A$, or the space $H^{\infty }$ of bounded analytic functions on the disc, or any of their even duals. Then $C(K,X)$ has the Dunford-Pettis property.References
- J. Bourgain, On the Dunford-Pettis property, Proc. Amer. Math. Soc. 81 (1981), no. 2, 265–272. MR 593470, DOI 10.1090/S0002-9939-1981-0593470-8
- J. Bourgain, New Banach space properties of the disc algebra and $H^{\infty }$, Acta Math. 152 (1984), no. 1-2, 1–48. MR 736210, DOI 10.1007/BF02392189
- J. Chaumat, Une généralisation d’un théorème de Dunford-Pettis, Université de Paris XI, Orsay, U.E.R. Mathématique no. 85, 1974.
- Cho-Ho Chu and Bruno Iochum, The Dunford-Pettis property in $C^*$-algebras, Studia Math. 97 (1990), no. 1, 59–64. MR 1074769, DOI 10.4064/sm-97-1-59-64
- Joe Diestel, A survey of results related to the Dunford-Pettis property, Proceedings of the Conference on Integration, Topology, and Geometry in Linear Spaces (Univ. North Carolina, Chapel Hill, N.C., 1979) Contemp. Math., vol. 2, Amer. Math. Soc., Providence, R.I., 1980, pp. 15–60. MR 621850
- J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964, DOI 10.1090/surv/015
- Reinhold Baer, Groups with Abelian norm quotient group, Amer. J. Math. 61 (1939), 700–708. MR 34, DOI 10.2307/2371324
- G. Emmanuele, Remarks on weak compactness of operators defined on certain injective tensor products, Proc. Amer. Math. Soc. 116 (1992), no. 2, 473–476. MR 1120506, DOI 10.1090/S0002-9939-1992-1120506-5
- J. Lindenstrauss and H. P. Rosenthal, The ${\cal L}_{p}$ spaces, Israel J. Math. 7 (1969), 325–349. MR 270119, DOI 10.1007/BF02788865
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces, Lecture Notes in Mathematics, Vol. 338, Springer-Verlag, Berlin-New York, 1973. MR 0415253
- Aleksander Pełczyński, Banach spaces of analytic functions and absolutely summing operators, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 30, American Mathematical Society, Providence, R.I., 1977. Expository lectures from the CBMS Regional Conference held at Kent State University, Kent, Ohio, July 11–16, 1976. MR 0511811, DOI 10.1090/cbms/030
- Elias Saab and Paulette Saab, On stability problems of some properties in Banach spaces, Function spaces (Edwardsville, IL, 1990) Lecture Notes in Pure and Appl. Math., vol. 136, Dekker, New York, 1992, pp. 367–394. MR 1152362
- Michel Talagrand, La propriété de Dunford-Pettis dans ${\cal C}(K,\,E)$ et $L^{1}(E)$, Israel J. Math. 44 (1983), no. 4, 317–321 (French, with English summary). MR 710236, DOI 10.1007/BF02761990
- P. Wojtaszczyk, Banach spaces for analysts, Cambridge Studies in Advanced Mathematics, vol. 25, Cambridge University Press, Cambridge, 1991. MR 1144277, DOI 10.1017/CBO9780511608735
Additional Information
- Manuel D. Contreras
- Affiliation: E. S. Ingenieros Industriales, Avda. Reina Mercedes s/n, 41012-Sevilla, Spain
- MR Author ID: 335888
- Email: contreras@cica.es
- Santiago Díaz
- Affiliation: E. S. Ingenieros Industriales, Avda. Reina Mercedes s/n, 41012-Sevilla, Spain
- MR Author ID: 310764
- Email: madrigal@cica.es
- Received by editor(s): January 6, 1995
- Received by editor(s) in revised form: May 9, 1995
- Additional Notes: This research has been partially supported by La Consejería de Educación y Ciencia de la Junta de Andalucía
- Communicated by: Theodore W. Gamelin
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3413-3416
- MSC (1991): Primary 46E15, 46E40; Secondary 46B03, 46B25
- DOI: https://doi.org/10.1090/S0002-9939-96-03436-3
- MathSciNet review: 1340380