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Displaying similar documents to “Riesz angles of Orlicz sequence spaces”

Stability of positive part of unit ball in Orlicz spaces

Ryszard Grzaślewicz, Witold Seredyński (2005)

Commentationes Mathematicae Universitatis Carolinae

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The aim of this paper is to investigate the stability of the positive part of the unit ball in Orlicz spaces, endowed with the Luxemburg norm. The convex set Q in a topological vector space is stable if the midpoint map Φ : Q × Q → Q , Φ ( x , y ) = ( x + y ) / 2 is open with respect to the inherited topology in Q . The main theorem is established: In the Orlicz space L ϕ ( μ ) the stability of the positive part of the unit ball is equivalent to the stability of the unit ball.

Sigma order continuity and best approximation in L ϱ -spaces

Shelby J. Kilmer, Wojciech M. Kozƚowski, Grzegorz Lewicki (1991)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we give a characterization of σ -order continuity of modular function spaces L ϱ in terms of the existence of best approximants by elements of order closed sublattices of L ϱ . We consider separately the case of Musielak–Orlicz spaces generated by non- σ -finite measures. Such spaces are not modular function spaces and the proofs require somewhat different methods.