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Remarks on the Istratescu measure of noncompactness.

Janusz Dronka — 1993

Collectanea Mathematica

In this paper we give estimations of Istratescu measure of noncompactness I(X) of a set X C lp(E1,...,En) in terms of measures I(Xj) (j=1,...,n) of projections Xj of X on Ej. Also a converse problem of finding a set X for which the measure I(X) satisfies the estimations under consideration is considered.

Growth functions for some uniformly amenable groups

Janusz Dronka; Bronislaw Wajnryb; Paweł Witowicz; Kamil Orzechowski — 2017

Open Mathematics

We present a simple constructive proof of the fact that every abelian discrete group is uniformly amenable. We improve the growth function obtained earlier and find the optimal growth function in a particular case. We also compute a growth function for some non-abelian uniformly amenable group.

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