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

Colloquium Mathematicae (1992)

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

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topBandyopadhyaya, 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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- [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] S. Mazur, Über schwache Konvergenz in den Räumen $\left({L}^{p}\right)$, Studia Math. 4 (1933), 128-133. Zbl59.1076.01
- [11] R. R. Phelps, A representation theorem for bounded convex sets, Proc. Amer. Math. Soc. 11 (1960), 976-983. Zbl0098.07904
- [12] A. Sersouri, The Mazur property for compact sets, Pacific J. Math. 133 (1988), 185-195. Zbl0653.46021
- [13] A. Sersouri, Mazur's intersection property for finite dimensional sets, Math. Ann. 283 (1989), 165-170. Zbl0642.52002
- [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] V. Zizler, Note on separation of convex sets, Czechoslovak Math. J. 21 (1971), 340-343. Zbl0218.46018
- [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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