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International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 52382, 12 pages
http://dx.doi.org/10.1155/2007/52382
Research Article

Multismoothness in Banach Spaces

114 MacLean Hall, University of Iowa, Iowa City, IA 52242, USA
2Stat-Math Unit, Indian Statistical Institute, R. V. College P.O., Bangalore 560059, India

Received 3 July 2007; Accepted 18 September 2007

Academic Editor: Andrei I. Volodin

Copyright © 2007 Bor-Luh Lin and T. S. S. R. K. Rao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Heĭnrih, “The differentiability of the norm in spaces of operators,” Funkcional'nyi Analiz i ego Priloženija, vol. 9, no. 4, pp. 93–94, 1975 (Russian). View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. W. Deeb and R. Khalil, “Exposed and smooth points of some classes of operation in L(lp),” Journal of Functional Analysis, vol. 103, no. 2, pp. 217–228, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. F. Kittaneh and R. Younis, “Smooth points of certain operator spaces,” Integral Equations and Operator Theory, vol. 13, no. 6, pp. 849–855, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. W. Werner, “Smooth points in some spaces of bounded operators,” Integral Equations and Operator Theory, vol. 15, no. 3, pp. 496–502, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. P. Harmand, D. Werner, and W. Werner, M-ideals in Banach spaces and Banach algebras, vol. 1547 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1993. View at Zentralblatt MATH · View at MathSciNet
  6. P. Bandyopadhyay, K. Jarosz, and T. S. S. R. K. Rao, “Unitaries in Banach spaces,” Illinois Journal of Mathematics, vol. 48, no. 1, pp. 339–351, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. G. Godefroy and T. S. S. R. K. Rao, “Renormings and extremal structures,” Illinois Journal of Mathematics, vol. 48, no. 3, pp. 1021–1029, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. R. Khalil and A. Saleh, “Multi-smooth points of finite order,” Missouri Journal of Mathematical Sciences, vol. 17, no. 2, pp. 76–87, 2005. View at Google Scholar
  9. L. Zheng and Y. D. Zhuang, “K-rotund complex normed linear spaces,” Journal of Mathematical Analysis and Applications, vol. 146, no. 2, pp. 540–545, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. P. Bandyopadhyay, V. P. Fonf, B.-L. Lin, and M. Martín, “Structure of nested sequences of balls in Banach spaces,” Houston Journal of Mathematics, vol. 29, no. 1, pp. 173–193, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. H. E. Lacey, The Isometric Theory of Classical Banach Spaces, vol. 208 of Die Grundlehren der mathematischen Wissenschaften, Springer, New York, NY, USA, 1974. View at Zentralblatt MATH · View at MathSciNet
  12. F. Sullivan, “Geometrical peoperties determined by the higher duals of a Banach space,” Illinois Journal of Mathematics, vol. 21, no. 2, pp. 315–331, 1977. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. B. Beauzamy and B. Maurey, “Points minimaux et ensembles optimaux dans les espaces de Banach,” Journal of Functional Analysis, vol. 24, no. 2, pp. 107–139, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Å. Lima, “Uniqueness of Hahn-Banach extensions and liftings of linear dependences,” Mathematica Scandinavica, vol. 53, no. 1, pp. 97–113, 1983. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. W. Ruess, “Duality and geometry of spaces of compact operators,” in Functional Analysis: Surveys and Recent Results, III (Paderborn, 1983), vol. 90 of North-Holland Math. Stud., pp. 59–78, North-Holland, Amsterdam, The Netherlands, 1984. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. A. J. Ellis, T. S. S. R. K. Rao, A. K. Roy, and U. Uttersrud, “Facial characterizations of complex Lindenstrauss spaces,” Transactions of the American Mathematical Society, vol. 268, no. 1, pp. 173–186, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. D. Narayana and T. S. S. R. K. Rao, “Transitivity of proximinality and norm attaining functionals,” Colloquium Mathematicum, vol. 104, no. 1, pp. 1–19, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. W. Deeb and R. Khalil, “Smooth points of vector valued function spaces,” The Rocky Mountain Journal of Mathematics, vol. 24, no. 2, pp. 505–512, 1994. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. E. M. Alfsen, Compact Convex Sets and Boundary Integrals, vol. 57 of Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer, New York, NY, USA, 1971. View at Zentralblatt MATH · View at MathSciNet