We study the extendibility of integral vector-valued polynomials on Banach spaces. We prove that an X-valued Pietsch-integral polynomial on E extends to an X-valued Pietsch-integral polynomial on any space F containing E, with the same integral norm. This is not the case for Grothendieck-integral polynomials: they do not always extend to X-valued Grothendieck-integral polynomials. However, they...

In this paper we obtain some practical criteria to bound the multiplication operator in Sobolev spaces with respect to measures in curves. As a consequence of these results, we characterize the weighted Sobolev spaces with bounded multiplication operator, for a large class of weights. To have bounded multiplication operator has important consequences in Approximation Theory: it implies the unif...

In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...

The core of the theory of absolutely summing operators lie in the ideas of A. Grothendieck in the 1950s. Further work (after a decade) of A. Pietsch [19] and Lindenstrauss and Pe l czyński [9] clarified Grothendiecks insights and nowadays the ideal of absolutely summing operators is a central topic of investigation. For details on absolutely summing operators we refer to the book by Diestel-Jar...

We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly uniformly continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Vald...

Let A be a unital Banach algebra, and denote the spectral radius of f ∈ A by ρ(f). If A is a uniform algebra and ρ(fh + 1) = ρ(gh + 1) for all h ∈ A, then it can be shown that f = g, a result that also carries in algebras of bounded linear operators on Banach spaces. On the other hand ρ(fh) = ρ(gh) does not imply f = g in any unital algebra, marking a distinction between the polynomials p(z, w)...