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More on the Kechris-Pestov-Todorcevic correspondence: Precompact expansions

L. Nguyen Van Thé (2013)

Fundamenta Mathematicae

In 2005, the paper [KPT05] by Kechris, Pestov and Todorcevic provided a powerful tool to compute an invariant of topological groups known as the universal minimal flow. This immediately led to an explicit representation of this invariant in many concrete cases. However, in some particular situations, the framework of [KPT05] does not allow one to perform the computation directly, but only after a slight modification of the original argument. The purpose of the present paper is to supplement [KPT05]...

Moscow spaces, Pestov-Tkačenko Problem, and C -embeddings

Aleksander V. Arhangel'skii (2000)

Commentationes Mathematicae Universitatis Carolinae

We show that there exists an Abelian topological group G such that the operations in G cannot be extended to the Dieudonné completion μ G of the space G in such a way that G becomes a topological subgroup of the topological group μ G . This provides a complete answer to a question of V.G. Pestov and M.G. Tkačenko, dating back to 1985. We also identify new large classes of topological groups for which such an extension is possible. The technique developed also allows to find many new solutions to the...

Most random walks on nilpotent groups are mixing

R. Rębowski (1992)

Annales Polonici Mathematici

Let G be a second countable locally compact nilpotent group. It is shown that for every norm completely mixing (n.c.m.) random walk μ, αμ + (1-α)ν is n.c.m. for 0 < α ≤ 1, ν ∈ P(G). In particular, a generic stochastic convolution operator on G is n.c.m.

Multiplicateurs de Mikhlin pour une classe particulière de groupes non-unimodulaires

Sami Mustapha (1998)

Annales de l'institut Fourier

On montre, pour une classe particulière de groupes non-unimodulaires G = N , où N est un groupe de Lie stratifié et où l’action de est définie par les dilatations naturelles de N , et pour les sous-laplaciens invariants à gauche correspondants Δ , que toute fonction m H 2 + ϵ ( ) possédant un support compact dans + définit un opérateur m ( Δ ) borné sur les espaces de Lebesgue L p ( G , d r g ) associés à la mesure de Haar invariante à droite sur G , 1 p .

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