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Journal of Function Spaces and Applications
Volume 2013, Article ID 187536, 19 pages
http://dx.doi.org/10.1155/2013/187536
Research Article

Köthe-Bochner Spaces and Some Geometric Properties Related to Rotundity and Smoothness

Department of Mathematics, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany

Received 24 May 2013; Accepted 27 June 2013

Academic Editor: T. S. S. R. K. Rao

Copyright © 2013 Jan-David Hardtke. 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. M. A. Smith, “Some examples concerning rotundity in Banach spaces,” Mathematische Annalen, vol. 233, no. 2, pp. 155–161, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. M. Fabian, P. Habala, P. Hájak et al., Functional Analysis and Infinite-Dimensional Geometry, CMS Books in Mathematics, Springer, New York, NY, USA, 2001.
  3. V. Kadets, R. Shvydkoy, G. Sirotkin, and D. Werner, “Banach spaces with the Daugavet property,” Transactions of the American Mathematical Society, vol. 352, no. 2, pp. 855–873, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. D. Hardtke, “Absolute sums of Banach spaces and some geometric properties related to rotundity and smoothness,” http://arxiv.org/abs/1201.2300.
  5. G. G. Sirotkin, “New properties of Lebesgue-Bochner Lp(Ω,Σ,μ;X) spaces,” Houston Journal of Mathematics, vol. 27, no. 4, pp. 897–906, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. K. S. Lau, “Best approximation by closed sets in Banach spaces,” Journal of Approximation Theory, vol. 23, no. 1, pp. 29–36, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. Gao, “Normal structure and modulus of u-convexity in Banach spaces,” in Function Spaces, Differential Operators and Nonlinear Analysis, pp. 195–199, Prometheus, Prague, Czech Republic, 1996. View at Google Scholar · View at MathSciNet
  8. S. Dhompongsa, A. Kaewkhao, and S. Saejung, “Uniform smoothness and U-convexity of ψ-direct sums,” Journal of Nonlinear and Convex Analysis, vol. 6, no. 2, pp. 327–338, 2005. View at Google Scholar · View at MathSciNet
  9. B. Beauzamy, Introduction to Banach Spaces and Their Geometry, North-Holland, Amsterdam, The Netherlands, 2nd edition, 1983. View at MathSciNet
  10. Y. A. Abramovich, C. D. Aliprantis, and O. Burkinshaw, “The Daugavet equation in uniformly convex Banach spaces,” Journal of Functional Analysis, vol. 97, no. 1, pp. 215–230, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. P. K. Lin, Köthe-Bochner Function Spaces, Birkhäauser, Boston, Mass, USA, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  12. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, vol. 2, Springer, Berlin, Germany, 1979. View at MathSciNet
  13. A. V. Bukhvalov, “On an analytic representation of operators with abstract norm,” Soviet Mathematics Doklady, vol. 14, pp. 197–201, 1973. View at Google Scholar
  14. G. Emmanuele and A. Villani, “Lifting of rotundity properties from E to Lp(μ,E),” The Rocky Mountain Journal of Mathematics, vol. 17, no. 3, pp. 617–627, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. M. Fabian and S. Lajara, “Smooth renormings of the Lebesgue-Bochner function space L1(μ,X),” Studia Mathematica, vol. 209, no. 3, pp. 247–265, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. A. Kamińska and B. Turett, “Rotundity in Köthe spaces of vector-valued functions,” Canadian Journal of Mathematics, vol. 41, no. 4, pp. 659–675, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. M. A. Smith and B. Turett, “Rotundity in Lebesgue-Bochner function spaces,” Transactions of the American Mathematical Society, vol. 257, no. 1, pp. 105–118, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. P. R. Halmos, Measure Theory, The University Series in Higher Mathematics, D. Van Nostrand, New York, NY, USA, 1950. View at MathSciNet
  19. N. L. Carothers, A Short Course on Banach Space Theory, vol. 64 of London Mathematical Society Student Texts, Cambridge University Press, Cambridge, UK, 2010. View at MathSciNet
  20. M. M. Day, “Uniform convexity. III,” Bulletin of the American Mathematical Society, vol. 49, no. 10, pp. 745–750, 1943. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. S. Dhompongsa, A. Kaewkhao, and S. Tasena, “On a generalized James constant,” Journal of Mathematical Analysis and Applications, vol. 285, no. 2, pp. 419–435, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. K. W. Anderson, Midpoint local uniform convexity, and other geometric properties of Banach spaces [Ph.D. dissertation], University of Illinois, 1960.
  23. P. N. Dowling and S. Saejung, “Extremal structure of the unit ball of direct sums of Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 4, pp. 951–955, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. A. R. Lovaglia, “Locally uniformly convex Banach spaces,” Transactions of the American Mathematical Society, vol. 78, no. 1, pp. 225–238, 1955. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet