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

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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.

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Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 39, No. 4, pp. 89–92, 2005

Original Russian Text Copyright © by Y. Q. Yan

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Yan, Y.Q. The Exact Value of Normal Structure Coefficients and WCS coefficients in a Class of Orlicz Function Spaces. Funct Anal Its Appl 39, 321–323 (2005). https://doi.org/10.1007/s10688-005-0056-y

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  • DOI: https://doi.org/10.1007/s10688-005-0056-y

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