The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Notes on approximation in the Musielak-Orlicz sequence spaces of multifunctions”

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

Ghassan Alherk, Henryk Hudzik (1994)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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...

Some approximation results in Musielak-Orlicz spaces

Ahmed Youssfi, Youssef Ahmida (2020)

Czechoslovak Mathematical Journal

Similarity:

We prove the continuity in norm of the translation operator in the Musielak-Orlicz L M spaces. An application to the convergence in norm of approximate identities is given, whereby we prove density results of the smooth functions in L M , in both the modular and norm topologies. These density results are then applied to obtain basic topological properties.

Topological dual of non-locally convex Orlicz-Bochner spaces

Marian Nowak (1999)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let L ϕ ( X ) be an Orlicz-Bochner space defined by an Orlicz function ϕ taking only finite values (not necessarily convex) over a σ -finite atomless measure space. It is proved that the topological dual L ϕ ( X ) * of L ϕ ( X ) can be represented in the form: L ϕ ( X ) * = L ϕ ( X ) n ∼ ⊕ L ϕ ( X ) s ∼ , where L ϕ ( X ) n ∼ and L ϕ ( X ) s ∼ denote the order continuous dual and the singular dual of L ϕ ( X ) respectively. The spaces L ϕ ( X ) * , L ϕ ( X ) n ∼ and L ϕ ( X ) s ∼ are examined by means of the H. Nakano’s theory of conjugate modulars. (Studia Mathematica 31 (1968), 439–449). The well known results of the...