The paper studies the core-Walras equivalence problem in the commodity space framework of Banach spaces, allocations being defined as Pettis integrable functions. In particular, a core-Walras equivalence result for a certain class of commodity spaces is established, without requiring that the commodity space be separable. The class covered by this result includes the Lp(μ) spaces, 1 ≤ p < ∞, μ ...

We study the extension of linear operators with range in a C(K)space, comparing and contrasting our results with the corresponding results for the nonlinear problem of extending Lipschitz maps with values in a C(K)space. We give necessary and sufficient conditions on a separable Banach space X which ensure that every operator T : E → C(K) defined on a subspace may be extended to an operator e T...

This article investigates the approximate controllability of second order non-autonomous functional evolution equations involving non-instantaneous impulses and nonlocal conditions. First, we discuss linear system in detail, which lacks existing literature. Then, derive sufficient conditions for our separable reflexive Banach spaces via operator, resolvent operator conditions, Schauder’s fixed ...

s: Plenary Speakers Spiros Argyros (National Technical University of Athens, Greece) [email protected] HI extensions of L∞ spaces and spaces with very few operators Tuesday, July 30, HA4, 9:00–9:50 We will present a general method of embedding Banach spaces with separable dual into L∞ spaces admitting very few operators. In particular we will discuss the following two results. Theorem 1. (i...

It is shown, using the Borwein–Preiss variational principle that for every continuous convex function f on a weakly compactly generated space X, every x0 ∈ X and every weakly compact convex symmetric set K such that spanK = X, there is a point of Gâteaux differentiability of f in x0 +K. This extends a Klee’s result for separable spaces. The well-known Mazur’s theorem says that a continuous conv...

We use Baire categorical arguments to construct dramatically pathological locally Lipschitz functions. The origins of this approach can be traced back to Banach and Mazurkiewicz (1931) who independently used similar categorical arguments to show that \almost every continuous real-valued function deened on 0,1] is nowhere diierentiable". As with the results of Banach and Mazurkiewicz, it appears...

This work introduces operator space analogues of the Separable Extension Property (SEP) for Banach spaces; the Complete Separable Extension Property (CSEP) and the Complete Separable Complemention Property (CSCP). The results use the technique of a new proof of Sobczyk’s Theorem, which also yields new results for the SEP in the non-separable situation, e.g., (⊕∞ n=1 Zn)c0 has the (2 + ε)-SEP fo...

We investigate for a bounded semigroup of linear operators S on Banach space E and vector x∈E, when relative compactness S(I−T)x every T∈S implies the orbit Sx. In particular, we derive characterizations separable spaces not containing c0 reflexivity with Schauder basis in terms such results.

In the first part of the paper we study the structure of Banach spaces with a conditional spreading basis. The geometry of such spaces exhibit a striking resemblance to the geometry of James’ space. Further, we show that the averaging projections onto subspaces spanned by constant coefficient blocks with no gaps between supports are bounded. As a consequence, every Banach space with a spreading...