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Packing in Orlicz sequence spaces

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EN
We show how one can, in a unified way, calculate the Kottman and the packing constants of the Orlicz sequence space defined by an N-function, equipped with either the gauge or Orlicz norms. The values of these constants for a class of reflexive Orlicz sequence spaces are found, using a quantitative index of N-functions and some interpolation theorems. The exposition is essentially selfcontained.
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autor
  • Department of Mathematics, University of California, Riverside, California 92521, U.S.A., rao@math.ucr.edu
autor
  • Department of Mathematics, University of California, Riverside, California 92521, U.S.A.
  • Department of Mathematics, Suzhou University, 215006 Suzhou, P.R. China
Bibliografia
  • [1] J. A. C. Burlak, R. A. Rankin and A. P. Robertson, The packing of spheres in the space $ℓ_p$, Proc. Glasgow Math. Assoc. 4 (1958), 22-25.
  • [2] C. E. Cleaver, On the extension of Lipschitz-Hölder maps on Orlicz spaces, Studia Math. 42 (1972), 195-204.
  • [3] C. E. Cleaver, Packing spheres in Orlicz spaces, Pacific J. Math. 65 (1976), 325-335.
  • [4] T. Domínguez Benavides and R. J. Rodríguez, Some geometric coefficients in Orlicz sequence spaces, Nonlinear Anal. 20 (1993), 349-358.
  • [5] J. Elton and E. Odell, The unit ball of every infinite dimensional normed linear space contains a (1+ε)-separated sequence, Colloq. Math. 44 (1981), 105-109.
  • [6] H. Hudzik, Every nonreflexive Banach lattice has the packing constant equal to 1/2, Collect. Math. 44 (1993), 131-135.
  • [7] C. A. Kottman, Packing and reflexivity in Banach spaces, Trans. Amer. Math. Soc. 150 (1970), 565-576.
  • [8] M. A. Krasnosel'skiĭ and Ya. B. Rutickiĭ, Convex Functions and Orlicz Spaces, Noordhoff, Groningen, 1961.
  • [9] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, I and II, Springer, Berlin, 1977 and 1979.
  • [10] W. Orlicz, Linear Functional Analysis, World Sci., 1992. [Original 1963.]
  • [11] M. M. Rao, Interpolation, ergodicity and martingales, J. Math. Mech. 16 (1966), 543-567.
  • [12] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991.
  • [13] Z. D. Ren, Packing in Orlicz function spaces, Ph.D. Dissertation, University of California, Riverside, 1994.
  • [14] T. F. Wang, Packing constants of Orlicz sequence spaces, Chinese Ann. Math. Ser. A 8 (1987), 508-513 (in Chinese).
  • [15] T. F. Wang and Y. M. Liu, Packing constant of a type of sequence spaces, Comment. Math. Prace Mat. 30 (1990), 197-203.
  • [16] Y. N. Ye, Packing spheres in Orlicz sequence spaces, Chinese Ann. Math. Ser. A 4 (1983), 487-493 (in Chinese).
  • [17] Y. N. Ye and Y. H. Li, Geometric equivalence relation of reflexivity in Orlicz sequence space, Northeastern Math. J. 3 (1986), 309-323 (in Chinese).
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bwmeta1.element.bwnjournal-article-smv126i3p235bwm
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