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A characterization of weakly sequentially complete Banach lattices

A. W. Wickstead (1976)

Annales de l'institut Fourier

The equivalence of the two following properties is proved for every Banach lattice E :1) E is weakly sequentially complete.2) Every σ ( E * , E ) -Borel measurable linear functional on E is σ ( E * , E ) -continuous.

A new proof of James' sup theorem.

Marianne Morillon (2005)

Extracta Mathematicae

We provide a new proof of James' sup theorem for (non necessarily separable) Banach spaces. One of the ingredients is the following generalization of a theorem of Hagler and Johnson: "If a normed space E does not contain any asymptotically isometric copy of l1, then every bounded sequence of E' has a normalized l1-block sequence pointwise converging to 0".

A note on Banach spaces with 1 -saturated duals

Denny H. Leung (1996)

Commentationes Mathematicae Universitatis Carolinae

It is shown that there exists a Banach space with an unconditional basis which is not c 0 -saturated, but whose dual is 1 -saturated.

A notion of Orlicz spaces for vector valued functions

Gudrun Schappacher (2005)

Applications of Mathematics

The notion of the Orlicz space is generalized to spaces of Banach-space valued functions. A well-known generalization is based on N -functions of a real variable. We consider a more general setting based on spaces generated by convex functions defined on a Banach space. We investigate structural properties of these spaces, such as the role of the delta-growth conditions, separability, the closure of , and representations of the dual space.

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