We show that, in some cases, the projective and the injective tensor products of two Banach spaces do not have the Dunford-Pettis property (DPP). As a consequence, we obtain that (c0⊗̂πc0)∗∗ fails the DPP. Since (c0⊗̂πc0)∗ does enjoy it, this provides a new space with the DPP whose dual fails to have it. We also prove that, if E and F are L1-spaces, then E⊗̂ǫF has the DPP if and only if both E and...

A new investigation is launched into the problem of decision-making in the face of 'complete ignorance', and linked to the problem of social choice. In the first section the author introduces a set of properties which might characterize a criterion for decision-making under complete ignorance. Two of these properties are novel: 'independence of non-discriminating states', and 'weak pessimism'. ...

we introduce a new one-step iteration process to approximate common fixed points of twononexpansive mappings in banach spaces and prove weak convergence of the iterative sequence using (i)opial’s condition and (ii) kadec-klee property. strong convergence theorems are also established in banachspaces and uniformly convex banach spaces under the so-called condition ( a ), which is weaker thancom...

The existence of a global attractor in the natural energy space is proved for the semilinear wave equation utt + βut − ∆u + f(u) = 0 on a bounded domain Ω ⊂ R with Dirichlet boundary conditions. The nonlinear term f is supposed to satisfy an exponential growth condition for n = 2, and for n ≥ 3 the growth condition |f(u)| ≤ c0(|u|γ + 1), where 1 ≤ γ ≤ n n−2 . No Lipschitz condition on f is assu...

Let Mφ denote the set of Borel probability measures invariant under a topological action φ on a compact metrizable space X. For a continuous function f : X → R, a measure μ ∈ Mφ is called f -maximizing if ∫ f dμ = sup{ ∫ f dm : m ∈Mφ}. It is shown that if μ is any ergodic measure in Mφ, then there exists a continuous function whose unique maximizing measure is μ. More generally, if E is a non-e...