Dunford–Pettis sets
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- by Paul Lewis
- Proc. Amer. Math. Soc. 129 (2001), 3297-3302
- DOI: https://doi.org/10.1090/S0002-9939-01-05963-9
- Published electronically: April 2, 2001
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Abstract:
Bibasic sequences are used to study relative weak compactness and relative norm compactness of Dunford–Pettis sets.References
- Kevin T. Andrews, Dunford-Pettis sets in the space of Bochner integrable functions, Math. Ann. 241 (1979), no. 1, 35–41. MR 531148, DOI 10.1007/BF01406706
- Elizabeth M. Bator, Remarks on completely continuous operators, Bull. Polish Acad. Sci. Math. 37 (1989), no. 7-12, 409–413 (1990) (English, with Russian summary). MR 1101901
- C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151–164. MR 115069, DOI 10.4064/sm-17-2-151-164
- William J. Davis, David W. Dean, and Bor Luh Lin, Bibasic sequences and norming basic sequences, Trans. Amer. Math. Soc. 176 (1973), 89–102. MR 313763, DOI 10.1090/S0002-9947-1973-0313763-9
- 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
- Joseph Diestel, Sequences and series in Banach spaces, Graduate Texts in Mathematics, vol. 92, Springer-Verlag, New York, 1984. MR 737004, DOI 10.1007/978-1-4612-5200-9
- J. Elton, Weakly null normalized sequences in Banach spaces, Ph.D. dissertation, Yale, 1979.
- G. Emmanuele, Banach spaces in which Dunford-Pettis sets are relatively compact, Arch. Math. (Basel) 58 (1992), no. 5, 477–485. MR 1156580, DOI 10.1007/BF01190118
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 92, Springer-Verlag, Berlin-New York, 1977. Sequence spaces. MR 0500056
- A. Pełczyński, A proof of Eberlein-Šmulian theorem by an application of basic sequences, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 12 (1964), 543–548. MR 172091
- A. Pełczyński and I. Singer, On non-equivalent bases and conditional bases in Banach spaces, Studia Math. 25 (1964/65), 5–25. MR 179583, DOI 10.4064/sm-25-1-5-25
- Haskell P. Rosenthal, A characterization of Banach spaces containing $l^{1}$, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411–2413. MR 358307, DOI 10.1073/pnas.71.6.2411
- Haskell P. Rosenthal, Point-wise compact subsets of the first Baire class, Amer. J. Math. 99 (1977), no. 2, 362–378. MR 438113, DOI 10.2307/2373824
- Ivan Singer, Bases in Banach spaces. II, Editura Academiei Republicii Socialiste România, Bucharest; Springer-Verlag, Berlin-New York, 1981. MR 610799
Bibliographic Information
- Paul Lewis
- Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
- Email: Lewis@unt.edu
- Received by editor(s): April 14, 1998
- Received by editor(s) in revised form: March 15, 2000
- Published electronically: April 2, 2001
- Communicated by: Dale Alspach
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3297-3302
- MSC (2000): Primary 46B20; Secondary 46B15, 46B45
- DOI: https://doi.org/10.1090/S0002-9939-01-05963-9
- MathSciNet review: 1845005