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Tytuł artykułu

A new geometrical constant of Banach spaces and the uniform normal structure

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We introduce and study a new geometrical constant γXψ of a Banach space X, by using the notion of ψ-direct sum given in [Y. Takahashi, M. Kato and K.-S. Saito, J. Inequal. Appl. 7 (2002), 179-186]. At rst, we characterize uniform non- squareness in terms γXψ Moreover, we consider Banach spaces having uniform normal structure.
Rocznik
Strony
3--13
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
autor
  • Department of Applied Chemistry and Biotechnology, Faculty of Engineering, Niigata Institute of Technology Kashiwazaki, Niigata 945-1195, Japan, mitani@adm.niit.ac.jp
Bibliografia
  • [1] J. Banas and B. Rzepka, Functions related to convexity and smoothness of normed spaces, Rend. Circ. Mat. Palermo 46(2) (1997), no. 3, 395{424.
  • [2] B. Beauzamy, Introduction to Banach Spaces and Their Geometry, 2nd ed., North-Holland, Amsterdam-New York-Oxford, 1985.
  • [3] F. F. Bonsall and J. Duncan, Numerical Ranges II, London Math. Soc. Lecture Note Series, Vol.10, 1973.
  • [4] M. M. Day, Normed Linear Spaces, 3rd ed., in: Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 21, Springer-Verlag, New York, 1973.
  • [5] S. Dhompongsa, P. Piraisangjun and S. Saejung, Generalized Jordan-von Neumann constants and uniform normal structure, Bull. Austral. Math. Soc. 67 (2003), 225{240.
  • [6] P. N. Dowling, On convexity properties of -direct sums of Banach spaces, J. Math. Anal. Appl. 288 (2003), no. 2, 540{543.
  • [7] J. Gao, Normal structure and modulus of smoothness in Banach spaces, Nonlinear Funct. Anal. Appl. 8 (2003), no. 2, 233{241.
  • [8] J. Gao and K. S. Lau, On two classes of Banach spaces with uniform normal structure, Studia Math. 99 (1991), 41{56.
  • [9] M. Kato, K. -S. Saito and T. Tamura, On -direct sums of Banach spaces and convexity, J. Austral. Math. Soc. 75 (2003), 413-422.
  • [10] M. Kato, K. -S. Saito and T. Tamura, Uniform non-squareness of -direct sums of Banach spaces X _ Y , Math. Inequalities Appl. 7 (2004), 429-437.
  • [11] M. Kato, L. Maligranda and Y. Takahashi, On James and Jordan-von Neumann constants and the normal structure coe_cient of Banach spaces, Studia Math. 144 (2001), 275{295.
  • [12] M. A. Khamsi, Uniform smoothness implies super-normal structure property, Nonlinear Anal. 19 (1992) 1063-1069.
  • [13] R. E. Megginson, An Introduction to Banach Space Theory, Grad. Texts in Math. 183, Springer, New York, 1998.
  • [14] K.-I. Mitani and K.-S. Saito, A note on geometrical properties of Banach spaces using - direct sums, J. Math. Anal. Appl. 327 (2007), 898{907.
  • [15] K.-S. Saito and M. Kato, Uniform convexity of -direct sums of Banach spaces, J. Math. Anal. Appl. 277 (2003), 1{11.
  • [16] Y. Takahashi and M. Kato, Von Neumann-Jordan constant and uniformly non-square Banach spaces, Nihonkai Math. J. 9 (1998), 155{169.
  • [17] Y. Takahashi, M. Kato and K.-S. Saito, Strict convexity of absolute normes on C2 and direct sums of Banach spaces, J. Inequal. Appl. 7 (2002), 179{186.
  • [18] C. Yang and F. Wang, On a new geometric constant related to the von Neumann-Jordan constant, J. Math. Anal. Appl. 324 (2006), 555{565.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0011-0060
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