Related papers: Effective descent morphisms for Banach modules

Let $A$ be a Banach algebra and $A^{**}$ be the second dual of it. We show that by some new conditions, $A$ is weakly amenable whenever $A^{**}$ is weakly amenable. We will study this problem under generalization, that is, if $(n+2)-th$…

In this paper, a general hybrid fixed point theorem for the contractive mappings in generalized Banach spaces is proved via measure of weak non-compactness and it is further applied to fractional integral equations for proving the existence…

The aim of this article is to study effective Reifenberg theorems for measures in a Hilbert or Banach space. For Hilbert spaces, we see all the results from $\mathbb{R}^n$ continue to hold with no additional restrictions. For a general…

We show that a representation of a Banach algebra $A$ on a Banach space $X$ can be extended to a canonical representation of $A^{**}$ on $X$ if and only if certain orbit maps $A\to X$ are weakly compact. When this is the case, we show that…

We generalize the notion of summable Szlenk index from a Banach space to an arbitrary weak$^*$-compact set. We prove that a weak$^*$-compact set has summable Szlenk index if and only if its weak$^*$-closed, absolutely convex hull does. As a…

It is a longstanding problem whether every contractible Banach algebra is necessarily finite-dimensional. In this note, we confirm this for Banach algebras acting on Banach spaces with the uniform approximation property. This generalizes a…

A reflexive Banach space with an unconditional basis admits an equivalent $1$-unconditional $2R$ norm and embeds into a reflexive space with a $1$-symmetric $2R$ norm. Partial results on $1$-symmetric $2R$ renormings of spaces with a…

Let $\mathcal A$, $\mathcal B$ be Banach $\mathfrak A$-modules with compatible actions and $\mathcal M$ be a left Banach $\mathcal A$-$\mathfrak A$-module and a right Banach $\mathcal B$-$\mathfrak A$-module. In the current paper, we study…

Let $A$ be a Banach algebra and $A^{**}$ be the second dual of it. We show that by some new conditions, $A$ is weakly amenable whenever $A^{**}$ is weakly amenable. We will study this problem under generalization, that is, if $(n+2)-th$…

In this paper we give sharp extensions of convoluted solutions of wave equations in abstract Banach spaces. The main technique is to use the algebraic structure, for convolution products $\ast$ and $\ast_c$, of these solutions which are…

This paper develops a general theory for first-order descent methods whose search directions are restricted to a prescribed dictionary in a reflexive Banach space. Instead of assuming that the linear span of the dictionary is dense, as in…

We prove that subhomogeneous continuous Banach bundles over compact metrizable spaces are equivalent to Hilbert bundles, while examples show that the metrizability assumption cannot be dropped completely. This complements the parallel…

We show that every Banach space containing isomorphic copies of $c_0$ can be equivalently renormed so that every nonempty relatively weakly open subset of its unit ball has diameter 2 and, however, its unit ball still contains convex…

We show that a toroidal morphism can be reduced to a weakly semistable one in a universal way if we allow families to be modified to Deligne-Mumford stacks instead of schemes.

We are concerned about improvements of the modulus of convexity by renormings of a super-reflexive Banach space. Typically optimal results are beyond Pisier's power functions bounds $t^p$, with $p \geq 2$, and they are related to the notion…

We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with…

Let $R$ be a commutative ring, $M$ an $R$-module and $\varphi_a$ be the endomorphism of $M$ given by right multiplication by $a\in R$. We say that $M$ is {\it weakly-morphic} if $M/\varphi_a(M)\cong \ker(\varphi_a)$ as $R$-modules for every…

The aim of this paper is to establish strong convergence theorems for a strongly relatively nonexpansive sequence in a smooth and uniformly convex Banach space. Then we employ our results to approximate solutions of the zero point problem…

We compute the derived functors of (the functors associated to) the ideal of compact operators in Banach spaces and obtain new results about the extension and lifting of compact operators.

We provide sufficient conditions for a mapping between two Banach spaces to be a diffeomorphism using the approach of an auxiliary functional and also by the aid of a duality mapping corresponding to a normalization function. We simplify…