Related papers: Group Invariant Bounded Linear Functions on Dedeki…

In this paper we introduce the systematic study of invariant functions and equivariant mappings defined on Minkowski space under the action of the Lorentz group. We adapt some known results from the orthogonal group acting on the Euclidean…

We generalize the fixed-point property for discrete groups acting on convex cones given by Monod in \cite{monod} to topological groups. At first, we focus on describing this fixed-point property from a functional point of view, and then we…

We prove that the category of Dedekind $\sigma$-complete Riesz spaces is an infinitary variety, and we provide an explicit equational axiomatization. In fact, we show that finitely many axioms suffice over the usual equational…

For any real number $p\in [1,+\infty)$, we characterise the operations $\mathbb{R}^I \to \mathbb{R}$ that preserve $p$-integrability, i.e., the operations under which, for every measure $\mu$, the set $\mathcal{L}^p(\mu)$ is closed. We…

We prove an implicit function theorem for functions on infinite-dimensional Banach manifolds, invariant under the (local) action of a finite dimensional Lie group. Motivated by some geometric variational problems, we consider group actions…

We show that every non-precompact topological group admits a fixed point-free continuous action by affine isometries on a suitable Banach space. Thus, precompact groups are defined by the fixed point property for affine isometric actions on…

The concept of Hausdorff continuous interval valued functions, developed within the theory of Hausdorff approximations and originaly defined for interval valued functions of one real variable is extended to interval valued functions defined…

We pose some open problems related to boundedness of real-valued functions on balleans and coarse spaces. Also we prove that the Bergman property of groups is a coarse invariant. A special attention is payed to balleans on groups.

This work is motivated by a question published in E. Glasner's paper On a question of Kazhdan and Yom Din regarding the possibility to approximate functionals on a Banach space which are almost invariant with respect to an action of a…

In this paper, continuous binary operations of a topological space are studied and a criterion of their invertibility is proved. The classification problem of groups of invertible continuous binary operations of locally compact and locally…

In a topological Riesz space there are two types of bounded subsets: order bounded subsets and topologically bounded subsets. It is natural to ask (1) whether an order bounded subset is topologically bounded and (2) whether a topologically…

In this note we prove various sharp boundedness results on suitable Hardy type spaces for Riesz transforms of arbitrary order on noncompact symmetric spaces of arbitrary rank.

Given a Dedekind incomplete ordered field, a pair of convergent nets of gaps which are respectively increasing or decreasing to the same point is used to obtain a further equivalent criterion for Dedekind completeness of ordered fields:…

The celebrated Paley-Wiener theorem naturally identifies the spaces of bandlimited functions with subspaces of entire functions of exponential type. Recently, it has been shown that these spaces remain invariant only under composition with…

We study the Picard groups of connected linear algebraic groups, and especially the subgroup of translation-invariant line bundles. We prove that this subgroup is finite over every global function field. We also utilize our study of these…

In this paper we generalize a result in [1], showing that an arbitrary Riemannian symmetric space can be realized as a closed submanifold of a covering group of the Lie group defining the symmetric space. Some properties of the subgroups of…

This article gives an up-to-date account of the theory of discrete group actions on non-Riemannian homogeneous spaces. As an introduction of the motifs of this article, we begin by reviewing the current knowledge of possible global forms of…

We consider the Noether's problem on the noncommutative real rational functions invariant under the linear action of a finite group. For abelian groups the invariant skew-fields are always rational. We show that for a solvable group the…

We study orthogonally additive operators between Riesz spaces without the Dedekind completeness assumption on the range space. Our first result gives necessary and sufficient conditions on a pair of Riesz spaces $(E,F)$ for which every…

This paper builds on our previous work in which we showed that, for all connected semisimple linear Lie groups $G$ acting on a non-compactly causal symmetric space $M = G/H$, every irreducible unitary representation of $G$ can be realized…