Related papers: A Banach space in which every injective operator i…

We give examples of real Banach spaces with exactly infinite countably many complex structures and with $\omega_1$ many complex structures.

Given a separable Banach space $E$, we construct an extremely non-complex Banach space (i.e. a space satisfying that $\|Id + T^2\|=1+\|T^2\|$ for every bounded linear operator $T$ on it) whose dual contains $E^*$ as an $L$-summand. We also…

We examine the phenomenon when surjective algebra homomorphisms between algebras of operators on Banach spaces are automatically injective. In the first part of the paper we shall show that for certain Banach spaces $X$ the following…

In this paper we deal with two weaker forms of injectivity which turn out to have a rich structure behind: separable injectivity and universal separable injectivity. We show several structural and stability properties of these classes of…

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…

In this paper we study the reflexivity of a unital strongly closed algebra of operators with complemented invariant subspace lattice on a Banach space. We prove that if such an algebra contains a complete Boolean algebra of projections of…

Let $X$ be a compact Hausdorff space, let $E$ be a Banach space, and let $C(X,E)$ stand for the Banach space of $E$-valued continuous functions on $X$ under the uniform norm. In this paper we characterize Integral operators (in the sense of…

Let C(K) be the Banach space of all continuous functions on a given compact space K. We investigate the w*-sequential closure in C(K)* of the set of all finitely supported probabilities on K. We discuss the coincidence of the Baire…

We study the dynamics induced by an $m$-linear operator. We answer a question of B\`es and Conejero showing an example of an $m$-linear hypercyclic operator acting on a Banach space. Moreover we prove the existence of $m$-linear hypercyclic…

In this note a large class of primary Banach spaces is characterized. Namely, it will be demonstrated that under the Continuum Hypothesis the ultrapower of any infinite dimensional nonsuperreflexive Banach space is always primary.…

An infinite dimensional notion of asymptotic structure is considered. This notion is developed in terms of trees and branches on Banach spaces. Every countably infinite countably branching tree $\mathcal T$ of a certain type on a space X is…

We study order-to-weak continuous operators from an ordered Banach space to a normed space. It is proved that under rather mild conditions every order-to-weak continuous operator is bounded.

Let $E$, $F$ be separable Hilbert spaces, and assume that $E$ is infinite-dimensional. We show that for every continuous mapping $f:E\to F$ and every continuous function $\varepsilon: E\to (0, \infty)$ there exists a $C^{\infty}$ mapping…

Let $T:X\to X$ be a compact linear (or more generally affine) operator from a Banach space into itself. For each $x\in X$, the sequence of iterates $T^nx, n=0,1,...$ and its averages $\frac{1}{k}\sum_{k=0}^nT^{k-1}x, n=0,1,...$ are either…

It is proved that for every compact metric space $K$ there exists a Banach space $X$ whose Calkin algebra $\mathcal{L}(X)/\mathcal{K}(X)$ is homomorphically isometric to $C(K)$. This is achieved by appropriately modifying the…

We characterize all entire functions that transform a weighted Banach spaces of analytic functions $\mathcal{H}^{\infty}_{\mu_1}$ into another space of the same kind $\mathcal{H}^{\infty}_{\mu_2}$ by superposition for very general weights…

A new method of defining hereditarily indecomposable Banach spaces is presented. This method provides a unified approach for constructing reflexive HI spaces and also HI spaces with no reflexive subspace. All the spaces presented here…

Given a map $f \colon E \longrightarrow F$ between Banach spaces (or Banach lattices), a set $A$ of $E$-valued bounded sequences, ${\bf x} \in A$ and a vector topology $\tau$ on $F$, we investigate the existence of an infinite dimensional…

We systematically derive general properties of continuous and holomorphic functions with values in closed operators, allowing in particular for operators with empty resolvent set. We provide criteria for a given operator-valued function to…

We construct a continuous linear operator acting on the space of smooth functions on the real line without non-trivial invariant subspaces. This is a first example of such an operator acting on a Fr\'echet space without a continuous norm.…