Packing in Orlicz sequence spaces

M. Rao; Z. Ren

Studia Mathematica (1997)

  • Volume: 126, Issue: 3, page 235-251
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Rao, M., and Ren, Z.. "Packing in Orlicz sequence spaces." Studia Mathematica 126.3 (1997): 235-251. <http://eudml.org/doc/216453>.

@article{Rao1997,
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.},
author = {Rao, M., Ren, Z.},
journal = {Studia Mathematica},
keywords = {packing constant; quantitative index; interpolation; Kottman constant; Orlicz sequence spaces; gauge norm; Orlicz norm},
language = {eng},
number = {3},
pages = {235-251},
title = {Packing in Orlicz sequence spaces},
url = {http://eudml.org/doc/216453},
volume = {126},
year = {1997},
}

TY - JOUR
AU - Rao, M.
AU - Ren, Z.
TI - Packing in Orlicz sequence spaces
JO - Studia Mathematica
PY - 1997
VL - 126
IS - 3
SP - 235
EP - 251
AB - 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.
LA - eng
KW - packing constant; quantitative index; interpolation; Kottman constant; Orlicz sequence spaces; gauge norm; Orlicz norm
UR - http://eudml.org/doc/216453
ER -

References

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  11. [11] M. M. Rao, Interpolation, ergodicity and martingales, J. Math. Mech. 16 (1966), 543-567. Zbl0166.11704
  12. [12] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991. Zbl0724.46032
  13. [13] Z. D. Ren, Packing in Orlicz function spaces, Ph.D. Dissertation, University of California, Riverside, 1994. 
  14. [14] T. F. Wang, Packing constants of Orlicz sequence spaces, Chinese Ann. Math. Ser. A 8 (1987), 508-513 (in Chinese). Zbl0651.46029
  15. [15] T. F. Wang and Y. M. Liu, Packing constant of a type of sequence spaces, Comment. Math. Prace Mat. 30 (1990), 197-203. Zbl0756.46008
  16. [16] Y. N. Ye, Packing spheres in Orlicz sequence spaces, Chinese Ann. Math. Ser. A 4 (1983), 487-493 (in Chinese). 
  17. [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). Zbl0641.46008

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