Schur property and lP isomorphic copies in Musielak–Orlicz sequence spaces

Isomorphic and isometric copies of l∞(Γ) in duals of Banach spaces and Banach lattices

Let X and E be a Banach space and a real Banach lattice, respectively, and let Γ denote an infinite set. We give concise proofs of the following results: (1) The dual space X contains an isometric copy of c0 iff X contains an isometric copy of l∞, and (2) E contains a lattice-isometric copy of c0(Γ) iff E contains a lattice-isometric copy of l∞(Γ).

Property (a2) in Orlicz Sequence Spaces

In this paper, we introduce a new geometric property (A2) ∗ and we show that if a separable Banach space has property (A2) ∗ then both X and its dual X∗ have the weak fixed point property. Criteria for Orlicz spaces to have the properties (A2), (A ε 2) ∗ and (NUS∗) are given.

Schur-Pair Property and the Structure of Varietal Covering Groups

Totally probabilistic Lp spaces

In this paper, we introduce the notion of probabilistic valued measures as a generalization of non-negative measures and construct the corresponding Lp spaces, for distributions p > "0. It is alsoshown that if the distribution p satises p "1 then, as in the classical case, these spaces are completeprobabilistic normed spaces.

COMPLEMENTED COPIES OF l AND PELCZYNSKI’S PROPERTY (V) IN BOCHNER FUNCTION SPACES

Let X be a Banach space and (fn)n be a bounded sequence in L (X). We prove a complemented version of the celebrated Talagrand’s dichotomy i.e we show that if (en)n denotes the unit vector basis of c0, there exists a sequence gn ∈ conv(fn, fn+1, . . . ) such that for almost every ω, either the sequence (gn(ω)⊗en) is weakly Cauchy in X⊗̂πc0 or it is equivalent to the unit vector basis of l. We the...