Related papers: Asymptotics of Operator Semigroups via the Semigro…

Sz.-Nagy's famous theorem states that a bounded operator $T$ which acts on a complex Hilbert space $\mathcal{H}$ is similar to a unitary operator if and only if $T$ is invertible and both $T$ and $T^{-1}$ are power bounded. There is an…

We consider continuous semigroups of analytic functions $\{\Phi_t\}_{t\geq0}$ in the so-called Gordon-Hedenmalm class $\mathcal{G}$, that is, the family of analytic functions $\Phi:\mathbb C_+\to \mathbb C_+$ giving rise to bounded…

We prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator $T$ in the weighted Lebesgue scale…

We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time $T>0$ by taking into account the orbit of the initial value under the…

We use a method similar to ultraproducts to study the common fixed point of a left reversible semitopological semigroup acting on a Banach space. As an application, we prove a Bruck-type theorem for nearly uniformly convex Banach spaces to…

In the framework of Hilbert spaces we shall give necessary and sufficient conditions to define a Dirichlet-to-Neumann operator via Dirichlet principle. For singular Dirichlet-to-Neumann operators we will establish Laurent expansion near…

In this work, we revisit the Krein-Rutman theory for semigroups of positive operators in a Banach lattice framework and we provide some very general, efficient and handy results with constructive estimates about: the existence of a solution…

In this note we show that for analytic semigroups the so-called Weiss condition of uniform boundedness of the operators $Re(\lambda)^\einhalb C(\lambda+A)^{-1}, \qquad Re(\lambda)>0$ on the complex right half plane and weak Lebesgue…

Let $S$ be a semitopological semigroup, and let $C$ be a nonempty closed convex subset of a reflexive Banach space. Under some amenability conditions on $S$, we provide existence results of fixed points for several Bregman nonexpansive type…

Let G be a Lie group and E be a locally convex topological G-module. If E is sequentially complete, then E and its space of smooth vectors are modules for the algebra D(G) of compactly supported smooth functions on G. However, the module…

A continuous operator $T$ between two Banach lattices $E$ and $F$ is called almost order-weakly compact, whenever for each almost order bounded subset $A$ of $E$, $T(A)$ is a relatively weakly compact subset of $F$. In Theorem 4, we show…

We prove that finite-spectrum representations of compact quantum groups either in unital $C^*$-algebras $A$ or on Banach spaces $E$ exhibit the same Banach-space-modeled differential-geometric structure as their classical analogues: (a)…

This paper is dedicated to weighted composition semigroups on spaces of continuous functions and their subspaces. We consider semigroups induced by semiflows and semicocycles on Banach spaces $\mathcal{F}(\Omega)$ of continuous functions on…

We introduce almost periodic Banach--Malcev algebras as a non-associative extension of Bohr's classical theory. Our framework is based on the relative compactness of adjoint orbits $\{e^{t\,\mathrm{ad}(x)}(y)\}$, which yields the spectral…

In this article, we address a problem posed by F. Bayart regarding the existence of an infinite-dimensional closed vector subspace (excluding the null operator) within the set of supercyclic operators on Banach spaces. We resolve this…

We generalize several recent results concerning the asymptotic expansions of Bergman kernels to the framework of geometric quantization and establish an asymptotic symplectic identification property. More precisely, we study the asymptotic…

We use the notion of $\A$-compact sets, which are determined by a Banach operator ideal $\A$, to show that most classic results of certain approximation properties and several Banach operator ideals can be systematically studied under this…

Every new inner product in a Hilbert space is obtained from the original one by means of a unique positive operator$.$ The first part of the paper is a survey on applications of such a technique, including a characterization of similarity…

We consider two $C_0$-semigroups $(e^{tA})_{t \ge 0}$ and $(e^{tB})_{t \ge 0}$ on function spaces (or, more generally, on Banach lattices) and analyse eventual domination between them in the sense that $|e^{tA}f| \le e^{tB}|f|$ for all…

We study frequent hypercyclicity in the context of strongly continuous semigroups of operators. More precisely, we give a criterion (sufficient condition) for a semigroup to be frequently hypercyclic, whose formulation depends on the Pettis…