ArticleOriginal scientific text

Title

Evaluation maps, restriction maps, and compactness

Authors 1, 1, 2

Affiliations

  1. Department of Mathematics, University of North Texas, Denton, Texas 76203-5116 U.S.A.
  2. Department of Mathematics Hardin-Simmens University Abilene, Texas 79698 U.S.A.

Bibliography

  1. D. Amir and J. Lindenstrauss, The structure of weakly compact sets in Banach spaces, Ann. of Math. 88 (1968), 35-46.
  2. K. Andrews, Dunford-Pettis sets in the space of Bochner integrable functions, Math. Ann. 241 (1979), 35-41.
  3. R. G. Bartle, N. Dunford and J. Schwartz, Weak compactness and vector measures, Canad. J. Math. 7 (1955), 289-305.
  4. E. M. Bator, Remarks on completely continuous operators, Bull. Polish Acad. Sci. Math. 37 (1987), 409-413.
  5. C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151-164.
  6. R. G. Bilyeu and P. W. Lewis, Some mapping properties of representing measures, Ann. Mat. Pura Appl. 109 (1976), 273-287.
  7. R. G. Bilyeu and P. W. Lewis, Vector measures and weakly compact operators on continuous function spaces: A survey, in: Measure Theory and its Applications, Proc. Measure Theory Conf., DeKalb, Ill., 1980, G. A. Goldin and R. F. Wheeler (eds.), Northern Illinois Univ., DeKalb, Ill, 1981, 165-172.
  8. F. Bombal, On (V*) sets and Pełczyński's property (V*), Glasgow Math. J. 32 (1990), 109-120.
  9. F. Bombal, On (V) and (V*) sets in vector-valued function spaces, preprint.
  10. J. Bourgain and F. Delbaen, A class of special calL spaces, Acta Math. 145 (1981), 155-176.
  11. J. Bourgain and J. Diestel, Limited operators and strict cosingularity, Math. Nachr. 119 (1984), 55-58.
  12. J. Diestel, Sequences and Series in Banach Spaces, Grad. Texts in Math. 92, Springer, 1984.
  13. J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, R.I., 1977.
  14. S. Dineen, Complex Analysis in Locally Convex Spaces, North-Holland Math. Stud. 57, North-Holland, New York, 1981.
  15. N. Dunford and J. T. Schwartz, Linear Operators. I. General Theory, Pure and Appl. Math. 7, Interscience, New York, 1958.
  16. J. Elton and E. Odell, The unit ball of every infinite-dimensional normed linear space contains a (1+ ε)-separated sequence, Colloq. Math. 44 (1981), 105-109.
  17. G. Emmanuele, A dual characterization of Banach spaces not containing l1, Bull. Polish Acad. Sci. Math. 34 (1986), 155-160.
  18. G. Emmanuele, On the reciprocal Dunford-Pettis property in projective tensor products, Math. Proc. Cambridge Philos. Soc. 109 (1991), 161-166.
  19. G. Emmanuele, Banach spaces on which Dunford-Pettis sets are relatively compact, Arch. Math. (Basel) 58 (1992), 477-485.
  20. G. Emmanuele, personal communication.
  21. A. Grothendieck, Sur les applications linéaires faiblement compactes d'espaces du type C(K), Canad. J. Math. 5 (1953), 129-173.
  22. J. Hagler and W. B. Johnson, On Banach spaces whose dual balls are not weak* sequentially compact, Israel J. Math. 28 (1977), 325-330.
  23. R. C. James, A non-reflexive Banach space isometric with its second conjugate, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 174-177.
  24. R. C. James, Separable conjugate spaces, Pacific J. Math. 10 (1960), 563-571.
  25. T. Leavelle, The reciprocal Dunford-Pettis and Radon-Nikodym properties in Banach spaces, Ph.D. dissertation, Univ. of North Texas, 1984.
  26. E. Odell and H. P. Rosenthal, A double-dual characterization of separable Banach spaces containing l1, Israel J. Math. 20 (1975), 375-384.
  27. A. Pełczyński, Banach spaces on which every unconditionally converging operator is weakly compact, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 10 (1962), 641-648.
  28. A. Pełczyński, On strictly singular and stictly cosingular operators. II, ibid. 13 (1965), 37-41.
  29. H. Rosenthal, A characterization of Banach spaces containing l1, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411-2413.
  30. H. Rosenthal, Pointwise compact subsets of the first Baire class, Amer. J. Math. 99 (1977), 362-378.
  31. E. Saab, Some characterizations of weak Radon-Nikodym sets, Proc. Amer. Math. Soc. 86 (1982), 307-311.
  32. I. Singer, Bases in Banach Spaces II, Springer, 1981.
Pages:
1-17
Main language of publication
English
Received
1997-09-30
Published
1998
Exact and natural sciences