Related papers: Maximal subspaces of strong continuity for composi…
We study the Lipschitz continuity of pluriharmonic Bloch mappings in the unit ball $\mathbb{B}^n$ with respect to the Bergman metric. We apply this to obtain a sufficient condition such that the composition operator on the pluriharmonic…
We study continuity and equicontinuity of semigroups on norming dual pairs with respect to topologies defined in terms of the duality. In particular, we address the question whether continuity of a semigroup already implies (local/quasi)…
We give necessary and sufficient conditions for a real-valued quasiconvex function f on a Baire topological vector space X (in particular, Banach or Frechet space) to be continuous at the points of a residual subset of X. These conditions…
The main aim of this paper is to introduce and analyze the notions of subspace almost periodicity and subspace weak almost periodicity for $C$-distribution semigroups and $C$-distribution cosine functions in Banach spaces. We continue our…
We consider semi-group BMO spaces associated with an arbitrary $\sigma$-finite von Neumann algebra $(\mathcal{M}, \varphi)$. We prove that the associated row and column BMO spaces always admit a predual, extending results from the finite…
We study continuity and H\"older continuity of $t\mapsto P_tf$, where $P_t$ is a generalized Mehler semigroup in $C_b(X)$, the space of the continuous and bounded functions from a Banach space $X$ to $R$, and $f\in C_b(X)$. The generators…
Generalizations of the theorems of Eberlein and Grothendieck on the precompactness of subsets of function spaces are considered: if $X$ is a countably compact space and $C_p(X)$ is a space of continuous functions in the pointwise topology…
The purpose of this article is to study the problem of finding sharp lower bounds for the norm of the product of polynomials in the ultraproducts of Banach spaces $(X_i)_{\mathfrak U}$. We show that, under certain hypotheses, there is a…
The symmetric inverse monoid $I_X$ on a set $X$ consists of all bijective functions whose domain and range are subsets of $X$ under the usual composition and inversion of partial functions. For an arbitrary infinite set $X$, we classify all…
We extend some classical results of Cowling and Meda to the noncommutative setting. Let $(T_t)_{t>0}$ be a symmetric contraction semigroup on a noncommutative space $L_p(\mathcal{M}),$ and let the functions $\phi$ and $\psi$ be regularly…
Suppose $\varphi$ is a holomorphic self map of the unit disk and $C_\varphi$ is a composition operator with symbol $\varphi$ that fixes the origin and $0<|\varphi'(0)|<1$. This work explores sufficient conditions that ensure all holomorphic…
In the context of general Banach spaces characterizations for the maximal monotonicity of operators with non-empty domain interior as well as stronger continuity properties for such operators are provided.
This paper is based on three hours of lectures given by the first author in the "Focus Program on Analytic Function Spaces and their Applications" July 1 -- December 31, 2021, organized by the Fields Institute for Research in Mathematical…
The notion of $p$-summing Bloch mapping from the complex unit open disc $\mathbb{D}$ into a complex Banach space $X$ is introduced for any $1\leq p\leq\infty$. It is shown that the linear space of such mappings, equipped with a natural…
In this note we connect the notion of solutions of a martingale problem to the notion of a strongly continuous and locally equi-continuous semigroup on the space of bounded continuous functions equipped with the strict topology. This…
In this paper we study the separately continuous actions of semitopological monoids on pseudocompact spaces. The main aim of this paper is to generalize Lawson's results to some class of pseudocompact spaces. Also, we introduce a concept of…
This paper explores the interactions of absolute continuity of the (quasi)norm with the concepts that are fundamental in the theory of rearrangement-invariant (quasi-)Banach function spaces, such as the Luxemburg representation or the…
We study the existence of continuous (linear) operators from the Banach spaces $\mbox{Lip}_0(M)$ of Lipschitz functions on infinite metric spaces $M$ vanishing at a distinguished point and from their predual spaces $\mathcal{F}(M)$ onto…
In this paper we lay the foundations for the Morse theoretical study of strongly indefinite functionals on Banach manifolds by developing the local theory for a specific model class that captures several key analytical features also arising…
A Banach space $X$ has the ball fixed point property (BFPP) if for every closed ball $B$ and for every nonexpansive mapping $T\colon B\to B$, there is a fixed point. We study the BFPP for $C(K)$-spaces. Our goal is to determine topological…