Lower bounds for Jung constants of Orlicz sequence spaces

Z. D. Ren

Annales Polonici Mathematici, Tome 98 (2010), p. 23-34 / Harvested from The Polish Digital Mathematics Library

Résumé

A new lower bound for the Jung constant $JC(l^{(Φ)})$ of the Orlicz sequence space $l^{(Φ)}$ defined by an N-function Φ is found. It is proved that if $l^{(Φ)}$ is reflexive and the function tΦ’(t)/Φ(t) is increasing on $(0,Φ^{-1}(1)]$, then $JC(l^{(Φ)}) ≥ (Φ^{-1}(1/2))/(Φ^{-1}(1))$. Examples in Section 3 show that the above estimate is better than in Zhang’s paper (2003) in some cases and that the results given in Yan’s paper (2004) are not accurate.

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Publié le : 2010-01-01

Zbl 1194.46027

EUDML-ID : urn:eudml:doc:280857