For every α < ω1 we establish the existence of a separable Banach space whose Szlenk index is ω and which is universal for all separable Banach spaces whose Szlenkindex does not exceed ω. In order to prove that result we provide an intrinsic characterization of which Banach spaces embed into a space admitting an FDD with upper estimates.

We construct one-step iterative process for an α- nonexpansive mapping and a mapping satisfying condition (C) in the framework of a convex metric space. We study △-convergence and strong convergence of the iterative process to the common fixed point of the mappings. Our results are new and are valid in hyperbolic spaces, CAT(0) spaces, Banach spaces and Hilbert spaces, simultaneously.

We analyze the construction of a sequence space Θ̃, resp. a sequence of sequence spaces, in order to have {gi} ∞ i=1 as a Θ̃-frame or Banach frame for a Banach space X , resp. pre-F -frame or F -frame for a Fréchet space XF = ∩s∈N0Xs, where {Xs}s∈N0 is a sequence of Banach spaces.

The purpose of this article is to prove existence of mass minimizing integral currents with prescribed possibly non-compact boundary in all dual Banach spaces and furthermore in certain spaces without linear structure, such as injective metric spaces and Hadamard spaces. We furthermore prove a weak -compactness theorem for integral currents in dual spaces of separable Banach spaces. Our theorem...

We study interpolation, generated by an abstract method of means, of bilinear operators between quasi-Banach spaces. It is shown that under suitable conditions on the type of these spaces and the boundedness of the classical convolution operator between the corresponding quasi-Banach sequence spaces, bilinear interpolation is possible. Applications to the classical real method spaces, Calderón-...

In this paper we study conditions on a Banach space X that ensure that the Banach algebra K(X) of compact operators is amenable. We give a symmetrized approximation property of X which is proved to be such a condition. This property is satisfied by a wide range of Banach spaces including all the classical spaces. We then investigate which constructions of new Banach spaces from old ones preserv...

The object of the investigation is to study reducible $M$-ideals in Banach spaces. It is shown that if the number of $M$-ideals in a Banach space $X$ is $n(<infty)$, then the number of reducible $M$-ideals does not exceed of $frac{(n-2)(n-3)}{2}$. Moreover, given a compact metric space $X$, we obtain a general form of a reducible $M$-ideal in the space $C(X)$ of continuous functions on $X$. The...

(A revised and expanded version of these notes are now published by Springer.) 1 Banach Spaces Definition A normed vector space X is a vector space over R or C with a function called the norm. 1. The set of real numbers with the norm taken to be the absolute value.

Keywords: Boundary value problems Differential-operator equations Banach-valued Besov spaces Operator-valued multipliers Interpolation of Banach spaces a b s t r a c t The boundary value problems for linear and nonlinear degenerate differential-operator equations in Banach-valued Besov spaces are studied. Several conditions for the separability of linear elliptic problems are given. Moreover, t...

Some weighted Ostrowski type integral inequalities for operators and vector-valued functions in Banach spaces are given. Applications for linear operators in Banach spaces and differential equations are also provided.