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On some properties of Musielak-Orlicz sequence spaces

Shragin I.V.

Commentationes Mathematicae

2008

Vol. 48, [Z] 2

147-153

We consider a nontrivial vector space X and a semimodularM : X→[0,∞] with property: [...] . The function M generates in X a metric d with [formula] At the same time M generates a metric in Musielak-Orlicz sequence space lM, namely [formula] It is proved that the space (lM, p) is complete if and only if the space (X, d) is complete. [formula] Several examples are considered.

Local uniform rotundity in Musielak-Orlicz sequence space equipped with the Luxemburg norm

Wang J.M., Liu X.B., Cui Y.A.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2006

Vol. 46, [Z] 1

131-139

In this paper, we present criteria for local uniform rotundity and weak local uniform rotundity in Musielak-Orlicz sequence spaces equipped with the Luxemburg norm.

Some Convexity properties in Musielak-Orlicz sequencespaces endowed with the Luxemburg Norm

Saejung S.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2005

Vol. 45, [Z] 1

75--90

Criteria for $k$-strict convexity, uniform convexity in everydirection, property K, property H, and property G inMusielak-Orlicz sequence spaces and their subspaces endowed withthe Luxemburg norm are presented. In particular, we obtain acharacterization of such properties of Nakano sequencespaces.

On some local geometry of Musielak-Orlicz sequence spaces

Dhompongsa S., Saejung S.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2003

[Z] 43(1)

43-62

Criteria for strong U-points, LUR-points, WLUR-points, CLUR-points and WCLUR-points in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm are given.