Lower bounds for Jung constants of Orlicz sequence spaces

Z. D. Ren¹

¹Department of Mathematics University of California Riverside, CA 92521, U.S.A.

Annales Polonici Mathematici, Volume 97 (2010) no. 1, pp. 23-34

Abstract

A new lower bound for the Jung constant $JC(l^{({\mit\Phi})})$ of the Orlicz sequence space $l^{({\mit\Phi})}$ defined by an $N$-function ${\mit\Phi}$ is found. It is proved that if $l^{({\mit\Phi})}$ is reflexive and the function $t{\mit\Phi}'(t)/{\mit\Phi}(t)$ is increasing on $(0,{\mit\Phi}^{-1}(1)]$, then $$ JC(l^{({\mit\Phi})})\geq \frac{{\mit\Phi}^{-1}({1}/{2})}{{\mit\Phi}^{-1}(1)}. $$ 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.

Article information

DOI: 10.4064/ap97-1-2

Keywords: lower bound jung constant mit phi orlicz sequence space mit phi defined n function mit phi found proved mit phi reflexive function mit phi mit phi increasing mit phi mit phi geq frac mit phi mit phi examples section above estimate better zhangs paper cases results given yans paper accurate