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### A Generalized Orlicz-Pettis Theorem and Applications.

Mathematische Zeitschrift

### A Large Bi-Invariant Nuclear Function Space on a Locally Compact Group.

Mathematica Scandinavica

### A Lebesgue decomposition for elements in a topological group.

International Journal of Mathematics and Mathematical Sciences

### Analysis on compact Lie groups of large dimension and on connected compact groups

Colloquium Mathematicae

The study of Gaussian convolution semigroups is a subject at the crossroad between abstract and concrete problems in harmonic analysis. This article suggests selected open problems that are in large part motivated by joint work with Alexander Bendikov.

### Borel Structures in Groups and Semigroups.

Mathematica Scandinavica

### Cardinal characteristics of the ideal of Haar null sets

Commentationes Mathematicae Universitatis Carolinae

We calculate the cardinal characteristics of the $\sigma$-ideal $ℋ𝒩\left(G\right)$ of Haar null subsets of a Polish non-locally compact group $G$ with invariant metric and show that $cov\left(ℋ𝒩\left(G\right)\right)\le 𝔟\le max\left\{𝔡,non\left(𝒩\right)\right\}\le non\left(ℋ𝒩\left(G\right)\right)\le cof\left(ℋ𝒩\left(G\right)\right)\phantom{\rule{-0.86pt}{0ex}}>\phantom{\rule{-0.86pt}{0ex}}min\left\{𝔡,non\left(𝒩\right)\right\}$. If $G={\prod }_{n\ge 0}{G}_{n}$ is the product of abelian locally compact groups ${G}_{n}$, then $add\left(ℋ𝒩\left(G\right)\right)=add\left(𝒩\right)$, $cov\left(ℋ𝒩\left(G\right)\right)=min\left\{𝔟,cov\left(𝒩\right)\right\}$, $non\left(ℋ𝒩\left(G\right)\right)=max\left\{𝔡,non\left(𝒩\right)\right\}$ and $cof\left(ℋ𝒩\left(G\right)\right)\ge cof\left(𝒩\right)$, where $𝒩$ is the ideal of Lebesgue null subsets on the real line. Martin Axiom implies that $cof\left(ℋ𝒩\left(G\right)\right)>{2}^{{\aleph }_{0}}$ and hence $G$ contains a Haar null subset that cannot be enlarged to a Borel or projective Haar null subset of $G$. This gives a negative (consistent) answer to a question of...

### Cauchy sequences in $ℒ$-groups

Czechoslovak Mathematical Journal

### Characterizing wirkfelder of certain classes of summability methods.

Journal für die reine und angewandte Mathematik

### Convexity and almost convexity in groups

Banach Center Publications

We give a review of results proved and published mostly in recent years, concerning real-valued convex functions as well as almost convex functions defined on a (not necessarily convex) subset of a group. Analogues of such classical results as the theorems of Jensen, Bernstein-Doetsch, Blumberg-Sierpiński, Ostrowski, and Mehdi are presented. A version of the Hahn-Banach theorem with a convex control function is proved, too. We also study some questions specific for the group setting, for instance...

### Dugundji spaces and topological groups

Commentationes Mathematicae Universitatis Carolinae

### Embedding a topological group into its WAP-compactification

Studia Mathematica

We prove that the topology of the additive group of the Banach space c₀ is not induced by weakly almost periodic functions or, what is the same, that this group cannot be represented as a group of isometries of a reflexive Banach space. We show, in contrast, that additive groups of Schwartz locally convex spaces are always representable as groups of isometries on some reflexive Banach space.

### Erratum - On the Bohr Compactification.

Mathematische Annalen

### Matrix entries of real representations of the groups $O\left(3\right)$ and $SO\left(3\right)$.

Sibirskij Matematicheskij Zhurnal

### Maximal convergences and minimal proper convergences in $\ell$-groups

Czechoslovak Mathematical Journal

### Normen auf freien topologischen Gruppen.

Mathematische Zeitschrift

### Objects Dual to Subsemigroups of Groups.

Monatshefte für Mathematik

### On a covering group theorem and its applications.

Lobachevskii Journal of Mathematics

### On a Generalised Open-Mapping Theorem

Mathematische Annalen

### On a generalization of Abelian sequential groups

Fundamenta Mathematicae

Let (G,τ) be a Hausdorff Abelian topological group. It is called an s-group (resp. a bs-group) if there is a set S of sequences in G such that τ is the finest Hausdorff (resp. precompact) group topology on G in which every sequence of S converges to zero. Characterizations of Abelian s- and bs-groups are given. If (G,τ) is a maximally almost periodic (MAP) Abelian s-group, then its Pontryagin dual group ${\left(G,\tau \right)}^{\wedge }$ is a dense -closed subgroup of the compact group ${\left({G}_{d}\right)}^{\wedge }$, where ${G}_{d}$ is the group G with the discrete...

### On characterized subgroups of Abelian topological groups $X$ and the group of all $X$-valued null sequences

Commentationes Mathematicae Universitatis Carolinae

Let $X$ be an Abelian topological group. A subgroup $H$ of $X$ is characterized if there is a sequence $𝐮=\left\{{u}_{n}\right\}$ in the dual group of $X$ such that $H=\left\{x\in X:\phantom{\rule{0.277778em}{0ex}}\left({u}_{n},x\right)\to 1\right\}$. We reduce the study of characterized subgroups of $X$ to the study of characterized subgroups of compact metrizable Abelian groups. Let ${c}_{0}\left(X\right)$ be the group of all $X$-valued null sequences and ${𝔲}_{0}$ be the uniform topology on ${c}_{0}\left(X\right)$. If $X$ is compact we prove that ${c}_{0}\left(X\right)$ is a characterized subgroup of ${X}^{ℕ}$ if and only if $X\cong {𝕋}^{n}×F$, where $n\ge 0$ and $F$ is a finite Abelian group. For every compact Abelian...

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