ArticleOriginal scientific text
Title
Packing in Orlicz sequence spaces
Authors 1, 1, 2
Affiliations
- Department of Mathematics, University of California, Riverside, California 92521, U.S.A.
- Department of Mathematics, Suzhou University, 215006 Suzhou, P.R. China
Abstract
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.
Keywords
packing constant, quantitative index, interpolation
Bibliography
- J. A. C. Burlak, R. A. Rankin and A. P. Robertson, The packing of spheres in the space
, Proc. Glasgow Math. Assoc. 4 (1958), 22-25. - C. E. Cleaver, On the extension of Lipschitz-Hölder maps on Orlicz spaces, Studia Math. 42 (1972), 195-204.
- C. E. Cleaver, Packing spheres in Orlicz spaces, Pacific J. Math. 65 (1976), 325-335.
- T. Domínguez Benavides and R. J. Rodríguez, Some geometric coefficients in Orlicz sequence spaces, Nonlinear Anal. 20 (1993), 349-358.
- 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.
- H. Hudzik, Every nonreflexive Banach lattice has the packing constant equal to 1/2, Collect. Math. 44 (1993), 131-135.
- C. A. Kottman, Packing and reflexivity in Banach spaces, Trans. Amer. Math. Soc. 150 (1970), 565-576.
- M. A. Krasnosel'skiĭ and Ya. B. Rutickiĭ, Convex Functions and Orlicz Spaces, Noordhoff, Groningen, 1961.
- J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, I and II, Springer, Berlin, 1977 and 1979.
- W. Orlicz, Linear Functional Analysis, World Sci., 1992. [Original 1963.]
- M. M. Rao, Interpolation, ergodicity and martingales, J. Math. Mech. 16 (1966), 543-567.
- M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991.
- Z. D. Ren, Packing in Orlicz function spaces, Ph.D. Dissertation, University of California, Riverside, 1994.
- T. F. Wang, Packing constants of Orlicz sequence spaces, Chinese Ann. Math. Ser. A 8 (1987), 508-513 (in Chinese).
- T. F. Wang and Y. M. Liu, Packing constant of a type of sequence spaces, Comment. Math. Prace Mat. 30 (1990), 197-203.
- Y. N. Ye, Packing spheres in Orlicz sequence spaces, Chinese Ann. Math. Ser. A 4 (1983), 487-493 (in Chinese).
- 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).