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Maluta’s coefficient and Opial’s properties in Musielak-Orlicz sequence spaces equipped with the Luxemburg norm. (English) Zbl 0922.46005
Consider $\varphi =(\varphi _{i})_{i=1}^{\infty }$ a Musielak-Orlicz function (i.e. $\varphi _{i}$ is a Orlicz function for every $i$) and $\ell ^{\varphi }=\{x\in \ell ^{0}\mid \sum_{i=1}^{\infty }\varphi _{i}(\lambda x_{i})<\infty $ for some $\lambda >0\}$ the Musielak-Orlicz sequence space. In the main results of the paper, when $\varphi $ is finitely valued and satisfies condition (*), the authors show that the Opial properties for $\ell ^{\varphi }$ are equivalent to the $\delta_2$ condition, and they give expressions for Maluta’s coefficient $D(\ell ^{\varphi })$ when $\ell ^{\varphi }$ is nonreflexive and reflexive, respectively.

MSC:
46A45Sequence spaces
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References:
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