Locally uniformly rotund renorming and fragmentability

Proceedings of the London Mathematical Society

Volumn 75, Issue 3, 1997, Pages 619-640

  Molto A ^a   Orihuela, J ^b   Troyanski, S ^a,c  

^a UNIVERSITY OF VALENCIA   (Spain)

^b UNIVERSITY OF MURCIA   (Spain)

^c UNIVERSITY OF SOFIA   (Bulgaria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33747076947     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024611597000452     Document Type: Article

References (27)

1. G. ALEXANDROV and V. BABEV, 'Banach spaces not isomorphic to weakly midpoint locally uniformly rotund spaces', C. R. Acad. Bulgare Sci. 41 (1988) 29-31.
2. ∞' (in Russian), Mathematics and mathematical education, proceedings of the 14th Spring Conference of the Union of Bulgarian Mathematicians, Sunny Beach 1985 (Bulgar. Akad. Nauk., Sofia, 1985), pp. 189-191.
3. R. DEVILLE, G. GODEFROY, and V. ZIZLER, Smoothness and renorming in Banach spaces, Pitman Monographs and Surveys in Pure and Applied Mathematics 64 (Longman Scientific & Technical, Harlow, 1993).
4. J. DIESTEL, 'Geometry of Banach spaces - selected topics', Lectures Notes in Mathematics 485 (Springer, Berlin, 1975).
5. G. GODEFROY, 'Existence de normes très lisses sur certains espaces de Banach', Bull. Sci. Math. 106 (1982) 63-68.
6. G. GODEFROY, S. TROYANSKI, J. WHITFIELD, and V. ZIZLER, 'Three space problem for locally uniformly rotund renormings of Banach spaces', Proc. Amer. Math. Soc. 94 (1985) 647-652.
7. R. HAYDON, 'Trees in renorming theory', Banach File Service, majordomo@Littlewood.math. okstate.edu (send message 'subscribe banach').
8. R. HAYDON, 'Countable unions of compact spaces with the Namioka property', Mathematika 41 (1994) 141-144.
9. R. HAYDON and C. A. ROGERS, 'A locally uniformly convex renorming for certain C(K)', Mathematika 37 (1990) 1-8.
10. J. E. JAYNE, I. NAMIOKA, and C. A. ROGERS, 'σ-fragmentable Banach spaces', Mathematika 39 (1992) 161-188, 197-215.
11. J. E. JAYNE, I. NAMIOKA, and C. A. ROGERS, 'Topological properties of Banach spaces', Proc. London Math. Soc. (3) 66 (1993) 651-672.
12. J. E. JAYNE, I. NAMIOKA, and C. A. ROGERS, 'σ-fragmented Banach spaces II', Studia Math. 111 (1994) 69-80.
13. J. E. JAYNE, I. NAMIOKA, and C. A. ROGERS, 'Continuous functions on compact totally ordered spaces', J. Funct. Anal. 134 (1995) 261-280.
14. J. E. JAYNE, J. ORIHUELA, A. J. PALLARÉS, and G. VERA, 'σ-fragmentability of multivalued maps and selection theorems', J. Funct. Anal. 117 (1993) 243-273.
15. J. L. KELLEY, General topology, Graduate Texts in Mathematics 27 (Springer, Berlin, 1955).
16. K. KUNEN and H. ROSENTHAL, 'Martingale proofs of some geometrical results in Banach space theory', Pacific J. Math. 100 (1982) 153-175.
17. G. LANCIEN, 'Dentability indices and locally uniformly convex renormings', Rocky Mountain J. Math. 23 (1993) 635-647.
18. G. LANCIEN, 'On uniformly convex and uniformly Kadec-Klee renormings', Serdica Math. J. 21 (1995) 1-18.
19. B. L. LIN, P. K. LIN, and S. L. TROYANSKI, 'Characterizations of denting points', Proc. Amer. Math. Soc. 102 (1988) 526-528.
20. L. ONCINA, 'Borel sets and σ-fragmentability of a Banach space', masters' degree thesis, University College London, 1996.
21. G. PISIER, 'Martingales with values in uniformly convex spaces', Israel J. Math. 20 (1975) 326-350.
22. H. ROSENTHAL, 'On the structure of non-dentable closed bounded convex sets', Adv. in Math. 70 (1988) 1-58.
23. B. S. SPAHN, 'Measurable selection problems in general Borel structures', doctoral thesis, Warsaw University, 1981.
24. V. V. SRIVATSA, 'Baire class 1 selectors for upper-semicontinuous set-valued maps', Trans. Amer. Math. Soc. 337 (1993) 609-624.
25. K. STROMBERG, Probability for analysts (Chapman & Hall, New York, 1994).
26. S. L. TROYANSKI, 'On locally uniformly convex and differentiable norms in certain non-separable Banach spaces', Studia Math. 37 (1971) 173-180.
27. S. L. TROYANSKI, 'On some generalizations of denting points', Israel J. Math. 88 (1994) 175-188.