If Z is a quotient of a subspace of a separable Banach space X, and V is any separable Banach space, then there is a Banach couple (A 0 , A 1) such that A 0 and A 1 are isometric to X ⊕ V , and any intermediate space obtained using the real or complex interpolation method contains a complemented subspace isomorphic to Z. Thus many properties of Banach spaces, including having non-trivial cotype...

In this paper, we consider a class of non-autonomous nonlinear evolution equations in separable reflexive Banach spaces. First, linear problem and establish the approximate controllability results by finding feedback control with help an optimal problem. We then for semilinear differential equation spaces using theory systems, properties resolvent operator Schauder's fixed point theorem. Finall...

We give a new proof of a recent characterization by Diaz and Mayoral of compactness in the Lebesgue-Bochner spaces L X , where X is a Banach space and 1 ≤ p < ∞, and extend the result to vector-valued Banach function spaces EX , where E is a Banach function space with order continuous norm. Let X be a Banach space. The problem of describing the compact sets in the Lebesgue-Bochner spaces LpX , ...

Abstract We show that for a given initial point the typical, in sense of Baire category, nonexpansive compact valued mapping F has following properties: there is unique sequence successive approximations and this converges to fixed . In case separable Banach spaces we typical residual set points have trajectory.

In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, x(·)(t) ∈ a.e. on I, x(t) ∈ S, ∀t ∈ I, x(0) = x₀ ∈ S, (∗), where S is a closed subset in a Banach space X, I = [0, T], (T > 0), F : I × S → X, is an upper semicontinuous set-valued mapping with convex values satisfying F(t, x) ⊂ c(t)(||x|| + ||x|| (p)K, ∀(t, x) ∈ I × S, whe...

 We study the notion of bounded approximate Connes-amenability for‎ ‎dual Banach algebras and characterize this type of algebras in terms‎ ‎of approximate diagonals‎. ‎We show that bounded approximate‎ ‎Connes-amenability of dual Banach algebras forces them to be unital‎. ‎For a separable dual Banach algebra‎, ‎we prove that bounded‎ ‎approximate Connes-amenability implies sequential approximat...

We show that a separable Banach space has the RadonNikodym Property (RNP) if and only if it is isomorphic to the limit of an inverse system, V1 ← V2 ← . . . ← Vk ← . . . , where the Vi’s are finite dimensional Banach spaces, and the bonding maps Vk−1 ← Vk are quotient maps. We also show that the inverse system can be chosen to be a good finite dimensional approximation (GFDA), a notion introduc...

The paper investigates the variation of the spectrum of operators in infinite dimensional Banach spaces. Consider the space of bounded operators on a separable Banach space when equipped with the strong operator topology, and the Polish space of compact subsets of the closed unit disc of the complex plane when equipped with the Hausdorff topology. Then, it is shown that the unit spectrum functi...