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AVERAGING PROPERTIES AND SPREADING MODELS

  • CHO, KYUGEUN (Center for Liberal Arts and Instruction Development Myong Ji University) ;
  • LEE, CHONGSUNG (Department of Mathematics education, Inha University)
  • Published : 2005.09.01

Abstract

In this paper, we study averaging properties in Banach spaces using the Brunel-Sucheston's spreading model. We show that the Schlumprecht space S does not have the Banach­Saks property and II is finitely representable in the Schlumprecht space S using the spreading model properties.

Keywords

References

  1. B. Beauzamy, Introduction to Banach spaces and their geometry, North-Holland, New York, 1985
  2. A. Brunel and L. Sucheston, On B-convex Banach spaces, Math. Systems Theory 7 (1974), 294-299 https://doi.org/10.1007/BF01795947
  3. K. G. Cho, Banach-Saks Property on Schlumprecht's space, (dissertation) (1997), Inha University
  4. P. Erdos and M. Magidor, A note on regular methods of summability and the Banach-Saks property, Proc. Amer. Math. Soc. 59 (1976), 232-234 https://doi.org/10.2307/2041474
  5. S. Kakutani, Weak convergence in uniformly convex spaces, Tohoku Math. J. 45 (1938), 188-193
  6. D. Kutzarova and P. K. Lin, Remarks about Schlumprecht space, Israel J.Math. 128 (1999), 2059-2068
  7. T. Nishiura and D. Waterman, Reflexivity and summability, Studia Math. 23 (1963), 53-57 https://doi.org/10.4064/sm-23-1-53-57
  8. N. Okada and T. Ito, Applications of spreading model to regular methods of summabilities an growth rate of Cesaro means, J. Math. Soc. Japan 44 (1992), 591-612 https://doi.org/10.2969/jmsj/04440591
  9. Th. Schlumprecht, An arbitrarily distortable Banach space, Israel J. Math. 76 (1991), 81-85 https://doi.org/10.1007/BF02782845