On James and Jordan-von Neumann constants and the normal structure coefficient of Banach spaces

Studia Mathematica

Volumn 144, Issue 3, 2001, Pages 275-295

  Kato, Mikio ^a   Maligranda, Lech ^b   Takahashi, Yasuji ^c  

^a KYUSHU INSTITUTE OF TECHNOLOGY   (Japan)

^b LULEÅ UNIVERSITY OF TECHNOLOGY   (Sweden)

^c OKAYAMA PREFECTURAL UNIVERSITY   (Japan)

Author keywords

Banach mazur distance; Fixed point property; James constant; Jordan von neumann constant; Normal structure coefficient; Uniformly convex spaces; Uniformly non square spaces; Uniformly smooth spaces

Indexed keywords

EID: 0035665071     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm144-3-5     Document Type: Article

References (42)

1. A. Ayerbe Toledano, T. Domínguez Benavides and G. López Acedo, Measures of Noncompactness in Metric fixed Point Theory, Oper. Theory Adv. Appl. 99, Birkhäuser, Basel, 1997.
2. J. B. Baillon and R. Schoneberg, Asymptotic normal structure and fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 81 (1981), 257-264.
3. B. Beauzamy, Introduction to Banach Spaces and their Geometry, 2nd ed., North-Holland, Amsterdam, 1985.
4. W. L. Bynum, A class of spaces lacking normal structure, Compositio Math. 25 (1972), 233-236.
5. _, Normal structure coefficients for Banach spaces, Pacific J. Math. 86 (1980), 427-436.
6. E. Casini, About some parameters of normed linear spaces, Atti. Acad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 80 (1986), 11-15.
7. J. A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), 396-414.
8. _, The von Neumann-Jordan constant for the Lebesgue spaces, Ann. of Math. 38 (1937), 114-115.
9. M. M. Day, Some characterizations of inner product spaces, Trans. Amer. Math. Soc. 62 (1947), 320-337.
10. _, Uniform convexity in factor and conjugate spaces, Ann. of Math. 45 (1944), 375-385.
11. p(Ω), Proc. Roy. Soc. Edinburgh Sect. A 117 (1991), 299-303.
12. p,q, Houston J. Math. 22 (1996), 89-100.
13. T. Figiel, On the moduli of convexity and smoothness, Studia Math. 56 (1976), 121-155.
14. S. Fitzpatrick and B. Reznick, Skewness in Banach spaces, Trans. Amer. Math. Soc. 275 (1983), 587-597.
15. J. Gao and K. S. Lau, On the geometry of spheres in normed linear spaces, J. Austral. Math. Soc. Ser. A 48 (1990), 101-112.
16. _, _, On two classes of Banach spaces with uniform normal structure, Studia Math. 99 (1991), 41-56.
17. K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Univ. Press, 1990.
18. N. M. Gulevich, Fixed points of nonexpansive mappings, J. Math. Sci. 79 (1996), 755-815.
19. R. C. James, Inner products in normed linear spaces, Bull. Amer. Math. Soc. 53 (1947), 559-566.
20. R. C. James, Uniformly non-square Banach spaces, Ann. of Math. 80 (1964), 542-550.
21. _, Some self-dual properties of normed linear spaces, in: Sympos. Infinite Dim. Topology (Baton Rouge, 1967), Ann. of Math. Stud. 69, Princeton Univ. Press, 1972, 159-175.
22. A. Jiménez-Melado and E. Llorens-Fuster, The fixed point property for some uniformly nonsquare Banach spaces, Boll. Un. Mat. Ital. A 10 (1996), 587-595.
23. P. Jordan and J. von Neumann, On inner products in linear metric spaces, Ann. of Math. 36 (1935), 719-723.
24. M. Kato, L. Maligranda and Y. Takahashi, Von Neumann-Jordan constant and some geometrical constants of Banach spaces, in: Nonlinear Analysis and Convex Analysis, Res. Inst. Math. Sci. 1031, Kyoto Univ., Kyoto, 1998, 68-74.
25. M. Kato and Y. Takahashi, On the von Neumann-Jordan constant for Banach spaces, Proc. Amer. Math. Soc. 125 (1997), 1055-1062.
26. _, _, Von Neumann-Jordan constant for Lebesgue-Bochner spaces, J. Inequal. Appl. 2 (1998), 89-97.
27. M. A. Khamsi, Uniform smoothness implies super-normal structure property, Non-linear Anal. 19 (1992), 1063-1069.
28. J. Lindenstrauss, On the modulus of smoothness and divergent series in Banach spaces, Michigan Math. J. 10 (1963), 241-252.
29. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I. Sequence Spaces, Springer, Berlin, 1977.
30. _, _, Classical Banach Spaces II. Function Spaces, Springer, Berlin, 1979.
31. L. Maligranda, Orlicz Spaces and Interpolation, Seminars in Math. 5, Univ. Estadual de Campinas, Campinas SP, 1989.
32. E. Maluta, Uniformly normal structure and related coefficients, Pacific J. Math. 111 (1984), 357-369.
33. B. Maurey et G. Pisier, Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach, Studia Math. 58 (1976), 45-90.
34. R. E. Megginson, An Introduction to Banach Space Theory, Grad. Texts in Math. 183, Springer, New York, 1998.
35. V. D. Milman, Geometric theory of Banach spaces. II. Geometry of the unit sphere, Uspekhi Mat. Nauk 26 (1971), no. 6, 73-149 (in Russian); English transl.: Russian Math. Surveys 26 (1971), no. 6, 79-163.
36. V. D. Milman, Geometric theory of Banach spaces. II. Geometry of the unit sphere, Uspekhi Mat. Nauk 26 (1971), no. 6, 73-149 (in Russian); English transl.: Russian Math. Surveys 26 (1971), no. 6, 79-163.
37. S. Prus, Some estimates for the normal structure coefficient in Banach spaces, Rend. Circ. Mat. Palermo 40 (1991), 128-135.
38. M. A. Smith and B. Turett, Some examples concerning normal and uniform normal structure in Banach spaces, J. Austral. Math. Soc. Ser. A 48 (1990), 223-234.
39. Y. Takahashi and M. Kato, Von Neumann-Jordan constant and uniformly non-square Banach spaces, Nihonkai Math. J. 9 (1998), 155-169.
40. N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Pitman Monographs Surveys Pure Appl. Math. 38, Longman Sci. & Tech. and Wiley, New York, 1989.
41. B. Turett, A dual view of a theorem of Baillon, in: Nonlinear Analysis and Applications, Lecture Notes in Pure and Appl. Math. 80, Dekker, 1982, 279-286.
42. P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Univ. Press, Cambridge, 1991.