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Dunford-Pettis sets


Author: Paul Lewis
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
Published electronically: April 2, 2001
MathSciNet review: 1845005
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Abstract: Bibasic sequences are used to study relative weak compactness and relative norm compactness of Dunford-Pettis sets.


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

  • 1. K. Andrews, Dunford-Pettis sets in the space of Bochner integrable functions, Math. Ann. 241(1979), 35-41. MR 80f:46041
  • 2. E. Bator, Remarks on completely continuous operators, Bull. Polish Acad. Sci. Math. 37(1989), 409-413. MR 93c:46031
  • 3. C. Bessaga and A. Pelczynski, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17(1958), 151-164. MR 22:5872
  • 4. W. J. Davis, D. W. Dean, and Bor-Luh Lin, Bibasic sequences and norming basic sequences, Trans. Amer. Math. Soc. 176(1973), 89-102. MR 47:2317
  • 5. J. Diestel, A survey of results related to the Dunford-Pettis property, Contemporary Math. 2(1980), 15-60. MR 82i:46023
  • 6. J. Diestel, Sequences and series in Banach spaces, Grad. Texts in Math., no 92, Springer-Verlag, 1984. MR 85i:46020
  • 7. J. Elton, Weakly null normalized sequences in Banach spaces, Ph.D. dissertation, Yale, 1979.
  • 8. G. Emmanuele, Banach spaces in which Dunford-Pettis sets are relatively compact, Arch. Math. 58(1992), 477-485. MR 93m:46014
  • 9. J. Lindenstrauss and L. Tzafriri, Classical Banach spaces I, Springer-Verlag, Berlin, 1977. MR 58:17766
  • 10. A. Pelczynski, A proof of the Eberlein-Smulian theorem by an application of basic sequences, Bull. Acad. Polon. Sci. 12(1964), 543-548. MR 30:2317
  • 11. A. Pelczynski and I. Singer, On non-equivalent bases and conditional bases in Banach spaces, Studia Math. 25(1964), 5-25. MR 31:3831
  • 12. H. Rosenthal, A characterization of Banach spaces containing $\ell^1$, Proc. Nat. Acad. Sci. (U.S.A) 71(1974), 2411-2413. MR 50:10773
  • 13. H. Rosenthal, Pointwise compact subsets of the first Baire class, Amer. J. Math. 99(1977), 362-378. MR 55:11032
  • 14. I. Singer, Bases in Banach spaces II, Springer-Verlag, Berlin, 1981. MR 82k:46024

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Additional Information

Paul Lewis
Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
Email: Lewis@unt.edu

DOI: https://doi.org/10.1090/S0002-9939-01-05963-9
Keywords: Bibasic sequences, Dunford--Pettis sets
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
Article copyright: © Copyright 2001 American Mathematical Society

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