Displaying similar documents to “Isometries of Musielak-Orlicz spaces II”

Copies of l 1 and c o in Musielak-Orlicz sequence spaces

Ghassan Alherk, Henryk Hudzik (1994)

Commentationes Mathematicae Universitatis Carolinae

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Criteria in order that a Musielak-Orlicz sequence space l Φ contains an isomorphic as well as an isomorphically isometric copy of l 1 are given. Moreover, it is proved that if Φ = ( Φ i ) , where Φ i are defined on a Banach space, X does not satisfy the δ 2 o -condition, then the Musielak-Orlicz sequence space l Φ ( X ) of X -valued sequences contains an almost isometric copy of c o . In the case of X = I R it is proved also that if l Φ contains an isomorphic copy of c o , then Φ does not satisfy the δ 2 o -condition. These results...

A characterization of Orlicz spaces isometric to Lp-spaces.

Grzegorz Lewicki (1997)

Collectanea Mathematica

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In this note we present an affirmative answer to the problem posed by M. Baronti and C. Franchetti (oral communication) concerning a characterization of Lp-spaces among Orlicz sequence spaces. In fact, we show a more general characterization of Orlicz spaces isometric to Lp-spaces.

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.