Metric Semigroups and Groups of Multisets

D.Y. Dolishniak; A.V. Zagorodnyuk

doi:10.15421/242430

Metric Semigroups and Groups of Multisets

D.Y. Dolishniak (Vasyl Stefanyk Precarpathian National University)
A.V. Zagorodnyuk (Vasyl Stefanyk Precarpathian National University), https://orcid.org/0000-0002-5554-4342

Abstract

We investigate the algebraic and topological properties of sets of complex multisets associated with Banach spaces having symmetric bases. We consider algebraic structures on the sets of multisets and compare some natural metrics on the (semi)groups of multisets. Also, we construct nonlinear analogs of the weighted backward shift operator on metric spaces of multisets, establish conditions of topological transitivity, and prove an analog of the Topological Transitivity Criterion for metric semigroups.

Keywords

symmetric functions on Banach spaces; metric semigroups of multisets; topological transitivity; hypercyclicity

MSC 2020

Pri 46B70, Sec 47A16, 22A05

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