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Some remarks on generalised lush spaces

Jan-David Hardtke (2015)

Studia Mathematica

D. Tan, X. Huang and R. Liu [Studia Math. 219 (2013)] recently introduced the notion of generalised lush (GL) spaces, which, at least for separable spaces, is a generalisation of the concept of lushness introduced by Boyko et al. [Math. Proc. Cambridge Philos. Soc. 142 (2007)]. The main result of D. Tan et al. is that every GL-space has the so called Mazur-Ulam property (MUP). In this note, we prove some further properties of GL-spaces, for example, every M-ideal in a...

Some remarks on the equality W ( E , F * ) = K ( E , F * )

Giovanni Emmanuele (1998)

Archivum Mathematicum

We show that the equality W ( E , F * ) = K ( E , F * ) is a necessary condition for the validity of certain results about isomorphic properties in the projective tensor product E ⊗ π F of two Banach spaces under some approximation property type assumptions.

Some results in representable Banach spaces.

Miguel Angel Canela (1988)

Publicacions Matemàtiques

Some results are presented, concerning a class of Banach spaces introduced by G. Godefroy and M. Talagrand, the representable Banach spaces. The main aspects considered here are the stability in forming tensor products, and the topological properties of the weak* dual unitball.

Some Structures Related to Metric Projections in Orlicz Spaces

Bor-Luh Lin, Zhongrui Shi (1999)

Colloquium Mathematicae

We discuss k-rotundity, weak k-rotundity, C-k-rotundity, weak C-k-rotundity, k-nearly uniform convexity, k-β property, C-I property, C-II property, C-III property and nearly uniform convexity both pointwise and global in Orlicz function spaces equipped with Luxemburg norm. Applications to continuity for the metric projection at a given point are given in Orlicz function spaces with Luxemburg norm.

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