Smooth, very smooth and strongly smooth points in Musielak-Orlicz function spaces equipped with the Luxemburg norm

Henryk Hudzik; L. Wang; Ting Fu Wang

Displaying similar documents to “Smooth, very smooth and strongly smooth points in Musielak-Orlicz function spaces equipped with the Luxemburg norm”

Smooth points of the unit sphere in Musielak-Orlicz function spaces equipped with the Luxemburg norm

Zenon Zbąszyniak (1994)

Commentationes Mathematicae Universitatis Carolinae

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There is given a criterion for an arbitrary element from the unit sphere of Musielak-Orlicz function space equipped with the Luxemburg norm to be a point of smoothness. Next, as a corollary, a criterion of smoothness of these spaces is given.

Erratum to the paper "Smooth points of Musielak-Orlicz sequence spaces equipped with the Luxemburg norm" (Colloq. Math. 65 (1993), 157-164)

Henryk Hudzik, Zenon Zbąszyniak (1993)

Colloquium Mathematicae

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Smoothness in Musielak-Orlicz spaces equipped with the Orlicz norm.

Henryk Hudzik, Zenon Zbaszyniak (1997)

Collectanea Mathematica

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A formula for the distance of an arbitrary element x in Musielak-Orlicz space L^Phi from the subspace E^Phi of order continuous elements is given for both (the Luxemburg and the Orlicz) norms. A formula for the norm in the dual space of L^Phi is given for any of these two norms. Criteria for smooth points and smoothness in L^Phi and E^Phi equipped with the Orlicz norm are presented.

Weak uniform rotundity of Musielak--Orlicz spaces

Małgorzata Doman (1991)

Commentationes Mathematicae Universitatis Carolinae

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We give necessary and sufficient conditions for weak uniform rotundity of Musielak–Orlicz spaces $L_{ϕ}$ with the Luxemburg norm. The result is a generalization of a theorem by Kami’nska and Kurc.