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Functional Analysis and Its Applications

, Volume 39, Issue 4, pp 321–323 | Cite as

The Exact Value of Normal Structure Coefficients and WCS coefficients in a Class of Orlicz Function Spaces

  • Y. Q. Yan
Article
  • 42 Downloads

Abstract

Let φ be an N-function. Then the normal structure coefficients N and the weakly convergent sequence coefficients WCS of the Orlicz function spaces L φ[0, 1] generated by φ and equipped with the Luxemburg and Orlicz norms have the following exact values. (i) If F φ(t) = t ϕ(t)/φ(t) is decreasing and 1 < C φ < 2 (where \(C_\Phi = \lim _{t \to + \infty } t\varphi (t)/\Phi (t)\)), then N(L (φ)[0, 1]) = N(L φ[0, 1]) = WCS(L (φ)[0, 1]) = WCS(L φ[0, 1]) = 21−1/Cφ. (ii) If F φ(t) is increasing and C φ > 2, then N(L (φ)[0, 1]) = N(L φ[0, 1]) = WCS(L (φ)[0, 1]) = WCS(L φ[0, 1]) = 21/Cφ.

Key words

Orlicz space WCS coefficient normal structure coefficient 

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Copyright information

© MAIK "Nauka/Interperiodica" 2005

Authors and Affiliations

  • Y. Q. Yan
    • 1
  1. 1.Department of MathematicsSuzhou UniversityP. R. China

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