Related papers: Some translation-invariant Banach function spaces …

We introduce the operators "modified limit" and "accumulation" on a Banach space, and we use this to define what we mean by being internally computable over the space. We prove that any externally computable function from a computable…

We give a characterization of the existence of copies of $c_{0}$ in Banach spaces in terms of indexes. As an application, we deduce new proofs of James Distortion theorem and Bessaga-Pe{\l}czynski theorem about weakly unconditionally Cauchy…

This paper is devoted to the study of the relatively compact sets in Quasi-Banach function spaces, providing an important improvement of the known results. As an application, we take the final step in establishing a relative compactness…

We obtain new uniqueness theorems for harmonic functions defined on the unit disc or in the half plane. These results are applied to obtain new resolvent descriptions of spectral subspaces of polynomially bounded groups of operators on…

In the paper we discuss conformable derivative behavior in arbitrary Banach spaces and clear the connection between two conformable derivatives of different order. As a consequence we obtain the important result that an abstract function…

We introduce the Banach spaces $\ell^p_{a,b}$ and $c_{0,a,b}$, of analytic functions on the unit disc, having normalized Schauder bases consisting of polynomials of the form $f_n(z)=(a_n+b_nz)z^n, ~~n\geq0$, where $\{f_n\}$ is assumed to be…

The following topics are presented in these notes: Elements of Banach algebras, Banach algebras of the form $L^1(G)$, where $G$ is a locally compact group, spectrum of elements of Banach algebras, the spectral theory of compact operators on…

We develop a functional calculus for $d$-tuples of non-commuting elements in a Banach algebra. The functions we apply are free analytic functions, that is nc functions that are bounded on certain polynomial polyhedra.

The new class of Banach spaces, so-called asymptotic $l_p$ spaces, is introduced and it is shown that every Banach space with bounded distortions contains a subspace from this class. The proof is based on an investigation of certain…

We present an example of an infinite dimensional separable space of affine continuous functions on a Choquet simplex that does not contain a subspace linearly isometric to $c$. This example disproves a result stated in M. Zippin. On some…

We construct an example of a real Banach space whose group of surjective isometries has no uniformly continuous one-parameter semigroups, but the group of surjective isometries of its dual contains infinitely many of them. Other examples…

We prove several abstract results giving general conditions under which subspaces of linear or multilinear operators on Banach spaces or Banach lattices are closed. Each of these abstract results is followed by concrete applications,…

This preprint concerns Banach spaces of functions converging at infinity. In particular, spaces of continuous functions, Lebesgue spaces and sequence spaces. In each framework we show versions of Riesz's representation theorem.

We prove in particular that Banach spaces of the form $C_0(\Omega)$, where $\Omega$ is a locally compact space, enjoy a quantitative version of the reciprocal Dunford-Pettis property.

We develop a functional framework suitable for the treatment of partial differential equations and variational problems on evolving families of Banach spaces. We propose a definition for the weak time derivative that does not rely on the…

A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those…

We create a new, functional calculus, approach to approximation of C_0-semigroups on Banach spaces. As an application of this approach, we obtain optimal convergence rates in classical approximation formulas for C_0-semigroups. In fact, our…

We describe a $\C$-linear additive *-autonomous category of Banach spaces. Please note that a correction has been appended to the original version 1 which is maintained here for reference. Also, a proposed example of a *-autonomous category…

We consider operators T : M_0 -> Z and T : M -> Z, where Z is a Banach space and (M_0, M) is a pair of Banach spaces belonging to a general construction in which M is defined by a "big-O" condition and M_0 is given by the corresponding…

We consider the cardinal invariant CG(X) of the minimal number of weakly compact subsets which generate a Banach space X. We study the behavior of this index when passing to subspaces, its relation with the Lindelof number in the weak…