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

Pradipta Bandyopadhyaya

Colloquium Mathematicae (1992)

  • Volume: 63, Issue: 1, page 45-56
  • ISSN: 0010-1354

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Bandyopadhyaya, Pradipta. "The Mazur intersection property for families of closed bounded convex sets in Banach spaces." Colloquium Mathematicae 63.1 (1992): 45-56. <http://eudml.org/doc/210133>.

@article{Bandyopadhyaya1992,
author = {Bandyopadhyaya, Pradipta},
journal = {Colloquium Mathematicae},
keywords = {duality map; points of continuity; Bochner $L^p$-spaces; (w*-) denting points; support mapping; norming subspaces; Mazur Intersection Property; Mazur intersection property; MIP; separation property; Lebesgue-Bochner space},
language = {eng},
number = {1},
pages = {45-56},
title = {The Mazur intersection property for families of closed bounded convex sets in Banach spaces},
url = {http://eudml.org/doc/210133},
volume = {63},
year = {1992},
}

TY - JOUR
AU - Bandyopadhyaya, Pradipta
TI - The Mazur intersection property for families of closed bounded convex sets in Banach spaces
JO - Colloquium Mathematicae
PY - 1992
VL - 63
IS - 1
SP - 45
EP - 56
LA - eng
KW - duality map; points of continuity; Bochner $L^p$-spaces; (w*-) denting points; support mapping; norming subspaces; Mazur Intersection Property; Mazur intersection property; MIP; separation property; Lebesgue-Bochner space
UR - http://eudml.org/doc/210133
ER -

References

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  1. [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. Zbl0728.46020
  2. [2] E. Bishop and R. R. Phelps, A proof that every Banach space is subreflexive, Bull. Amer. Math. Soc. 67 (1961), 97-98. Zbl0098.07905
  3. [3] B. Bollobás, An extension to the theorem of Bishop and Phelps, Bull. London Math. Soc. 2 (1970), 181-182. Zbl0217.45104
  4. [4] R. D. Bourgin, Geometric Aspects of Convex Sets with the Radon-Nikodým Property, Lecture Notes in Math. 993, Springer, 1983. Zbl0512.46017
  5. [5] G. Choquet, Lectures on Analysis, Vol. II, W. A. Benjamin, New York 1969. 
  6. [6] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, R.I., 1977. 
  7. [7] N. Dunford and J. T. Schwartz, Linear Operators, Vol. I, Interscience, New York 1958. Zbl0084.10402
  8. [8] J. R. Giles, Convex Analysis with Application in the Differentiation of Convex Functions, Pitman Adv. Publ. Program, Boston 1982. Zbl0486.46001
  9. [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. Zbl0373.46028
  10. [10] S. Mazur, Über schwache Konvergenz in den Räumen ( L p ) , Studia Math. 4 (1933), 128-133. Zbl59.1076.01
  11. [11] R. R. Phelps, A representation theorem for bounded convex sets, Proc. Amer. Math. Soc. 11 (1960), 976-983. Zbl0098.07904
  12. [12] A. Sersouri, The Mazur property for compact sets, Pacific J. Math. 133 (1988), 185-195. Zbl0653.46021
  13. [13] A. Sersouri, Mazur's intersection property for finite dimensional sets, Math. Ann. 283 (1989), 165-170. Zbl0642.52002
  14. [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. Zbl0609.46005
  15. [15] V. Zizler, Note on separation of convex sets, Czechoslovak Math. J. 21 (1971), 340-343. Zbl0218.46018
  16. [16] V. Zizler, Renorming concerning Mazur's intersection property of balls for weakly compact convex sets, Math. Ann. 276 (1986), 61-66. Zbl0587.46007

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