In this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the Hypercyclicity Criterion. We characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional Banach space .

We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in $L^p([0,1],E)$, where $E$ is a separable Banach space. The main ingredients used in the proof of our results are measure of noncompactness, Darbo and Schauder fixed point theorems. Finally, an application is proved to illustrate the results of this work. 

We show that the Lipschitz structure of a separable quasi-Banach space does not determine, in general, its linear structure. Using the notion of the Arens-Eells p-space over a metric space for 0 < p ≤ 1 we construct examples of separable quasi-Banach spaces which are Lipschitz isomorphic but not linearly isomorphic.

This paper is an investigation of the universal separable metric space up to isometry U discovered by Urysohn. A concrete construction of U as a metric subspace of the space C[0, 1] of functions from [0, 1] to the reals with the supremum metric is given. An answer is given to a question of Sierpiński on isometric embeddings of U in C[0, 1]. It is shown that the closed linear span of an isometri...

It is consistent with the axioms of set theory that for every metric space X which is isometric to some separable Banach space or to Urysohn’s universal separable metric space U the following holds: (?)X There exists a nowhere meager subspace of X of cardinality א1 and any two nowhere meager subsets of X of cardinality א1 are almost isometric to each other. As a corollary, it is consistent that...

The two main results are: A. If a Banach space X is complementably universal for all subspaces of c0 which have the bounded approximation property, then X∗ is non separable (and hence X does not embed into c0), B. There is no separable Banach space X such that every compact operator (between Banach spaces) factors through X. Theorem B solves a problem that dates from the 1970s.

A separable Banach space X contains l1 isomorphically if and only if X has a bounded fundamental total wc∗0-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded fundamental total wc∗0-biorthogonal system.

We show that if X is a separable Banach space (or more generally a Banach with an infinite-dimensional separable quotient) then there is a continuous mapping f : X → X such that the autonomous differential equation x′ = f(x) has no solution at any point. In order to put our results into context, let us start by formulating the classical theorem of Peano. Theorem 1. (Peano) Let X = R, f : R×X → ...

1. Introduction and notation. In this paper the word " local " is used in at least three different meanings. Our aim is to study local Banach spaces of Fréchet or other locally convex spaces, and it turns out that it is convenient to use the local theory of Banach spaces for this purpose. Recall that given a locally convex space E and a continuous seminorm p on E the completion of the normed sp...

We demonstrate that a reproducing kernel Hilbert or Banach space of functions on a separable absolute Borel space or an analytic subset of a Polish space is separable if it possesses a Borel measurable feature map.