Related papers: Abstract almost periodicity for group actions on u…

Let G be an algebraic group over a complete separable valued field k. We discuss the dynamics of the G-action on spaces of probability measures on algebraic G-varieties. We show that the stabilizers of measures are almost algebraic and the…

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…

The main aim of this paper is to consider the classes of quasi-asymptotically almost periodic functions and Stepanov quasi-asymptotically almost periodic functions in Banach spaces. These classes extend the well known classes of…

Our aim is to study weak star continuous representations of semigroup actions into the duals of ``good'' (e.g., reflexive and Asplund) Banach spaces. This approach leads to flow analogs of Eberlein and Radon-Nikodym compacta and a new class…

We organize fundamental properties of quasi-Hamiltonian spaces on which a finite group acts, and we apply them to the theory of moduli spaces of flat connections on an oriented compact surface with boundary.

Generalizing Block and Weinberger's characterization of amenability we introduce the notion of uniformly finite homology for a group action on a compact space and use it to give a homological characterization of topological amenability for…

In this paper, we analyze various classes of multi-dimensional almost periodic type functions in general metric. The main classes of functions under our consideration are $({\mathrm R}, {\mathcal B},{\mathcal P},L)$-multi-almost periodic…

We consider certain finite sets of circle-valued functions defined on intervals of real numbers and estimate how large the intervals must be for the values of these functions to be uniformly distributed in an approximate way. This is used…

We establish a connection between two well-studied spaces of countable groups: the space of group operations and the space of marked groups. This connection shows that the two spaces are equivalent in terms of generic properties in the…

The dual action of a locally compact abelian group, in the context of C*-algebraic bundles, is shown to satisfy an integrability property, similar to Rieffel's proper actions. The tools developed include a generalization of Bochner's…

In the paper under review, we introduce the notions of various types of generalized (asymptotical) almost periodicity with variable exponents. We define and thoroughly analyze an important subclass of (asymptotically) Stepanov almost…

For any $p\in[1,\infty)$, we prove that the set of simple functions taking at most $k$ different values is proximinal in B\"ochner spaces $L^p(X)$ whenever $X$ is a dual Banach space with $w^*$-sequentially compact unit ball. With…

We study amenability of definable and topological groups. Among our main technical tools is an elaboration on and strengthening of the Massicot-Wagner version of the stabilizer theorem, and some results around measures. As an application we…

For a topological group $G$, amenability can be characterized by the amenability of the convolution Banach algebra $L^1(G)$. Here a Banach algebra $A$ is called amenable if every bounded derivation from $A$ into any dual--type…

Let $M\subset B(\mathcal H)$ be a von Neumann algebra acting on the Hilbert space $\mathcal H$. We prove that $M$ is finite if and only if, for every $x\in M$ and for all vectors $\xi,\eta\in\mathcal H$, the coefficient function $u\mapsto…

We study the asymptotic behavior of almost-orbits of abstract evolution systems in Banach spaces with or without a Lipschitz assumption. In particular, we establish convergence, convergence in average and almost-convergence of almost-orbits…

The first part of this article is a brief survey of the properties of so-called almost interior points in ordered Banach spaces. Those vectors can be seen as a generalization of ``functions which are strictly positive almost everywhere'' on…

We consider measurable and topological dynamical systems over locally compact abelian groups. Our main observation relates convergence of Wiener-Wintner type averages to eigenvalues of the dynamical system in question. As a consequence we…

We consider metrizable ergodic topological dynamical systems over locally compact, $\sigma$-compact abelian groups. We study pure point spectrum via suitable notions of almost periodicity for the points of the dynamical system. More…

We investigate the interaction between Arens products on the bidual of a Banach algebra and structural regularity properties of functionals on the algebra. Building on the classical characterization of weakly almost periodic functionals via…