Related papers: A note on the maximal operator on Banach function …

The problem involving the extension of functions from a certain class and defined on subdomains of the ambient space to the whole space is an old and a well investigated theme in analysis. A related question whether the extensions that…

This paper is about certain linear subspaces of Banach SN spaces (that is to say Banach spaces which have a symmetric nonexpansive linear map into their dual spaces). We apply our results to monotone linear subspaces of the product of a…

In this paper we give growth estimates for $\|T^n\|$ for $n\to \infty$ in the case $T$ is a strongly Kreiss bounded operator on a UMD Banach space $X$. In several special cases we provide explicit growth rates. This includes known cases…

Bonet, Frerick, Peris and Wengenroth constructed a hypercyclic operator on the locally convex direct sum of countably many copies of the Banach space $\ell_1$. We extend this result. In particular, we show that there is a hypercyclic…

Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$ and $H_X({\mathbb R}^n)$ the Hardy space associated with $X$, and let $\alpha\in(0,n)$ and $\beta\in(1,\infty)$. In this article, assuming that the (powered) Hardy--Littlewood…

We present partial results to the following question: Does every infinite dimensional Banach space have an infinite dimensional subspace on which one can define an operator which is not a compact perturbation of a scalar multiplication?

In this paper we characterize multiplication operators induced by operator valued maps on Banach function spaces. We also study multiplication semigroups and stability of these operators.

We obtain a pointwise description of functions belonging to function spaces with the lattice property. In particular, it is valid for Banach function spaces provided that the Hardy-Littlewood maximal operator is bounded. We also study…

In this paper we develop a functional calculus for bounded operators defined on quaternionic Banach spaces. This calculus is based on the notion of slice-regularity, see \cite{gs}, and the key tools are a new resolvent operator and a new…

We present a simple proof of the maximal monotonicity of the subdifferential operator in general Banach spaces. Using the Fitzpatrick function the Rockafellar surjectivity theorem follows as a corollary.

We consider linear operators defined on a subspace of a complex Banach space into its topological antidual acting positively in a natural sense. The goal of this paper is to investigate of this kind of operators. The main theorem is a…

We study the Hardy-Littlewood maximal operator in the Musielak-Orlicz-Sobolev space $W^{1,\varphi}(\mathbb{R}^n)$. Under some natural assumptions on $\varphi$ we show that the maximal function is bounded and continuous in…

The numerical index of a Banach space is a geometric constant relating the numerical radius of bounded linear operators to their standard operator norm. In this paper, we study the continuity of the numerical index under two distinct…

This thesis addresses Pour-El and Richards' fourth question from their book "Computability in analysis and physics", concerning the relation between higher order recursion theory and computability in analysis. Among other things it is shown…

We study extreme contractions in the setting of finite-dimensional polyhedral Banach spaces. Motivated by the famous Krein-Milman Theorem, we prove that a \emph{rank one} norm one linear operator between such spaces can be expressed as a…

Previously unknown estimates of uniform continuity of projection operators in Banach space have been obtained. They can be used in the investigations of approximation methods, in particular, the method of quasisolutions, methods of…

We explore the relation between the orthogonality of bounded linear operators in the space of operators and that of elements in the ground space. To be precise, we study if $ T, A \in \mathbb{L}(\mathbb{X}, \mathbb{Y}) $ satisfy $ T \bot_B…

Let $X$, $Y$ be Banach spaces and let $\mathcal{L}(X,Y)$ be the space of bounded linear operators from $X$ to $Y$. We develop the theory of double operator integrals on $\mathcal{L}(X,Y)$ and apply this theory to obtain commutator estimates…

We study a hypercyclicity property of linear dynamical systems: a bounded linear operator T acting on a separable infinite-dimensional Banach space X is said to be hypercyclic if there exists a vector x in X such that {T^{n}x : n>0} is…

The duality of uniform approximation property for Banach spaces is well known. In this note, we establish, under the assumption of local reflexivity, the duality of uniform approximation property in the category of operator spaces.