Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Moduli of near convexity of the Baernstein space


Authors: Józef Banaś, Leszek Olszowy and Kishin Sadarangani
Journal: Proc. Amer. Math. Soc. 123 (1995), 3693-3699
MSC: Primary 46B20; Secondary 47H09
DOI: https://doi.org/10.1090/S0002-9939-1995-1277094-5
MathSciNet review: 1277094
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we give the exact formulas for the so-called moduli of near convexity of the Baernstein space. This space is frequently used in the geometric theory of Banach spaces and in other branches of nonlinar functional analysis.


References [Enhancements On Off] (What's this?)

  • [1] R. R. Akmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina, and B. N. Sadovskii, Measures of noncompactness and condensing operators, Birkhäuser Verlag, Basel, Boston and Berlin, 1992. MR 1153247 (92k:47104)
  • [2] A. Baernstein II, On reflexivity and summability, Studia Math. 42 (1972), 91-94. MR 0305044 (46:4174)
  • [3] J. Banaś, On modulus of noncompact convexity and its properties, Canad. Math. Bull. 30 (1987), 186-192. MR 889537 (88f:46032)
  • [4] -, Compactness conditions in the geometric theory of Banach spaces, Nonlinear Anal. T.M.A. 16 (1991), 669-682. MR 1097324 (92b:46016)
  • [5] J. Banaś and K. Goebel, Measures of noncompactness in Banach spaces, Lecture Notes in Pure and Appl. Math., vol. 60, Marcel Dekker, New York and Basel, 1980. MR 591679 (82f:47066)
  • [6] Bor-Luh Lin and Pei-Kee Lin, A fully convex Banach space which does not have the Banach-Saks property, J. Math. Anal. Appl. 117 (1986), 273-283. MR 843018 (87i:46037)
  • [7] M. M. Day, Normed linear spaces, Ergeb. Math. Grenzgeb. (3), vol. 21, Springer-Verlag, Berlin and New York, 1973. MR 0344849 (49:9588)
  • [8] K. Deimling, Nonlinear functional analysis, Springer-Verlag, Berlin, 1985. MR 787404 (86j:47001)
  • [9] T. Dominguez Benavides and J. M. Ayerbe, Set-contractions and ball-contractions in $ {L^p}$-spaces, J. Math. Anal. Appl. 159 (1991), 500-507. MR 1120948 (92f:47058)
  • [10] K. Goebel and W. A. Kirk, Topics in metric fixed point theory, Cambridge Univ. Press, Cambridge, 1990. MR 1074005 (92c:47070)
  • [11] K. Goebel and T. Sekowski, The modulus of noncompact convexity, Ann. Univ. Mariae Curie-Sklodowska Sect. A 38 (1984), 41-48. MR 856623 (87j:46031)
  • [12] R. Huff, Banach spaces which are nearly uniformly convex, Rocky Mountain J. Math. 10 (1980), 743-749. MR 595102 (82b:46016)
  • [13] G. Köthe, Topological vector spaces I, Springer-Verlag, Berlin, 1969.
  • [14] D. Kutzarova, Every $ (\beta )$-space has the Banach-Saks property, C. R. Acad. Bulgar. Sci. 42 (1989), 9-12. MR 1037886 (91h:46027)
  • [15] D. Kutzarova, Bor-Luh Lin, and Wenyao Zhang, Some geometrical properties of Banach spaces related to nearly uniform convexity, Contemp. Math., vol. 144, Amer. Math. Soc., Providence, RI, 1993, pp. 165-171. MR 1209459 (94b:46021)
  • [16] J. R. Partington, On nearly uniformly convex Banach spaces, Math. Proc. Cambridge Philos. Soc. 93 (1983), 127-129. MR 684281 (84c:46017a)
  • [17] S. Rolewicz, On drop property, Studia Math. 85 (1987), 27-35. MR 879413 (88g:46033)
  • [18] C. J. Seifert, The dual of Baernstein space and the Banach-Saks property, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), 237-239. MR 0493276 (58:12305)
  • [19] T. Sekowski and A. Stachura, Noncompact smoothness and noncompact convexity, Atti Sem. Mat. Fis. Univ. Modena 36 (1988), 329-338. MR 976047 (90a:46040)
  • [20] M. M. Vainberg, Variational methods in the study of nonlinear operators, Holden-Day, San Francisco, 1964.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46B20, 47H09

Retrieve articles in all journals with MSC: 46B20, 47H09


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1277094-5
Keywords: Baernstein space, modulus of near convexity, measure of noncompactness
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society