Jung constants of Orlicz sequence spaces

Abstract

Abstract. Estimation of the Jung constants of Orlicz sequence spaces equipped with either the Luxemburg norm or the Orlicz norm is given. The exact values of the Jung constants of a class of reflexive Orlicz sequence spaces are found by using new quantitative indices for N -functions. Preliminaries. Let X be a normed linear space andBy using (2), Amir obtained the following.

On the upper bounds of WCS coefficients in Orlicz function spaces

“…In respect of the Jung constant of the Orlicz sequence space the author thinks that Zhang [15] (MR 2004b: 46020) is a detailed and valuable article.…”

Lower bounds for Jung constants of Orlicz sequence spaces

“…To illustrate Theorems 1 and 2 we present some examples, that were considered by Zhang [15] and Yan [14], except Example 4. In [10, p. 9] it was proved that F Φ (t) (= tΦ (t)/Φ(t)) is increasing on (0, ∞) and C 0 Φ = lim t→0 F Φ (t) = 2, so that Φ ∈ ∆ 2 (0) ∩ ∇ 2 (0).…”

“…It is known that for an N -function Φ, l (Φ) and l Φ are reflexive ⇔ Φ ∈ ∆ 2 (0) ∩ ∇ 2 (0). The Jung constants of l (Φ) and l Φ have been studied before by Zhang [15]. The main results in [15] can be summarized in the following two propositions.…”