Assuming the continuum hypothesis, we construct a universally weakly measurable function from [0,1] into a dual of some weakly compactly generated Banach space, which is not Pettis integrable. This… Expand

In the present note we introduce tame functionals on Banach algebras. A functional $f \in A^*$ on a Banach algebra $A$ is tame if the naturally defined linear operator $A \to A^*, a \mapsto f \cdot… Expand

There is a rich literature describing integrability of multifunctions that take weakly compact convex subsets of a separable Banach space as their values. Most of the papers concern the Bochner type… Expand

We produce several situations where some natural subspaces of classical Banach spaces of functions over a compact abelian group contain the space $c_0$.

We prove that a Banach space E has the compact range property (CRP) if and only if, for any given C∗-algebra A, every absolutely summing operator from A into E is compact. Related results for… Expand

Following [3] we say that a Tychonoff space $X$ is an Ascoli space if every compact subset $\mathcal{K}$ of $C_k(X)$ is evenly continuous; this notion is closely related to the classical Ascoli… Expand

Abstract.In this paper we study the Birkhoff integral of functions f:Ω→X defined on a complete probability space (Ω,Σ,μ) with values in a Banach space X. We prove that if f is bounded then its… Expand

In large random economies with heterogeneous agents, a standard stochastic framework presumes a random macro state, combined with idiosyncratic micro shocks. This can be formally represented by a… Expand