Download PDF - The Mazur intersection property for families of closed bounded convex sets in Banach spacesAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

The Mazur intersection property for families of closed bounded convex sets in Banach spaces

Authors 1

Affiliations

  1. Division of Theoretical Statistics and Mathematics, Indian Statistical Institute, 203 Barrackpore Trunk Road, Calcutta 700 035, India

Keywords

ENG
duality map, points of continuity, Bochner Lp-spaces, (w*-) denting points, support mapping, norming subspaces, Mazur Intersection Property

Bibliography

  1. P. Bandyopadhyaya and A. K. Roy, Some stability results for Banach spaces with the Mazur Intersection Property, Indag. Math. 1 (2) (1990), 137-154.
  2. E. Bishop and R. R. Phelps, A proof that every Banach space is subreflexive, Bull. Amer. Math. Soc. 67 (1961), 97-98.
  3. B. Bollobás, An extension to the theorem of Bishop and Phelps, Bull. London Math. Soc. 2 (1970), 181-182.
  4. R. D. Bourgin, Geometric Aspects of Convex Sets with the Radon-Nikodým Property, Lecture Notes in Math. 993, Springer, 1983.
  5. G. Choquet, Lectures on Analysis, Vol. II, W. A. Benjamin, New York 1969.
  6. J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, R.I., 1977.
  7. N. Dunford and J. T. Schwartz, Linear Operators, Vol. I, Interscience, New York 1958.
  8. J. R. Giles, Convex Analysis with Application in the Differentiation of Convex Functions, Pitman Adv. Publ. Program, Boston 1982.
  9. J. R. Giles, D. A. Gregory and B. Sims, Characterization of normed linear spaces with Mazur's intersection property, Bull. Austral. Math. Soc. 18 (1978), 105-123.
  10. S. Mazur, Über schwache Konvergenz in den Räumen (Lp), Studia Math. 4 (1933), 128-133.
  11. R. R. Phelps, A representation theorem for bounded convex sets, Proc. Amer. Math. Soc. 11 (1960), 976-983.
  12. A. Sersouri, The Mazur property for compact sets, Pacific J. Math. 133 (1988), 185-195.
  13. A. Sersouri, Mazur's intersection property for finite dimensional sets, Math. Ann. 283 (1989), 165-170.
  14. J. H. M. Whitfield and V. Zizler, Mazur's intersection property of balls for compact convex sets, Bull. Austral. Math. Soc. 35 (1987), 267-274.
  15. V. Zizler, Note on separation of convex sets, Czechoslovak Math. J. 21 (1971), 340-343.
  16. V. Zizler, Renorming concerning Mazur's intersection property of balls for weakly compact convex sets, Math. Ann. 276 (1986), 61-66.
Colloquium Mathematicum
1992/63/1
Export to PBN, Opens in new tab
Pages:
45-56
Main language of publication
English
Received
1990-10-05
Published
1992
Exact and natural sciences