WebA subset A of a semigroup S is called a chain (antichain) if ab∈{a,b} (ab∉{a,b}) for any (distinct) elements a,b∈A. A semigroup S is called periodic if for every element x∈S there exists n∈N such that xn is an idempotent. A semigroup S is called (anti)chain-finite if S contains no infinite (anti)chains. We prove that each antichain-finite semigroup S is … WebNov 28, 2024 · Taras Banakh, Vladimir Kadets Let be Banach spaces and , , be a continuous bilinear function, called a *Banach action*. We say that this action *preserves unconditional convergence* if for every bounded sequence in and unconditionally convergent series in the series is unconditionally convergent.
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WebMar 16, 2024 · [Submitted on 16 Mar 2024] Every 2-dimensional Banach space has the Mazur-Ulam property Taras Banakh We prove that every isometry between the unit spheres of 2-dimensional Banach spaces extends to a linear isometry of the Banach spaces. This resolves the famous Tingley's problem in the class of 2-dimensional Banach spaces. … WebJul 16, 2012 · TARAS BANAKH AND MAGDALENA NOWAK (Communicated by Alexander N. Dranishnikov) Abstract. Answering an old question of M. Hata, we construct an example of a 1-dimensional Peano continuum which is not homeomorphic to an attractor of IFS. A compact metric space X is called an IFS-attractor if X = (JH=i fi(X) f°r some contracting … look up ulta account
Banach actions preserving unconditional convergence
WebTaras Onufriovych Banakh MathSciNet Ph.D. Ivan Franko National University of Lviv 1993 Dissertation: Strong Universality in Locally-Convex Spaces and Bundles of Infinite … WebFeb 13, 2024 · Volume 6, issue 1, March 2024 Special Issue: Mathematics in the Banach Space Issue editors. Taras Banakh; Igor Chyzhykov; Anatolij Plichko; Valerii Samoilenko WebKey words and phrases. Zariski topology, topologizable group. 1 f2 TARAS BANAKH, IGOR PROTASOV As we already know, for an infinite group G, the topology ZG1 [x] , being cofinite, is non- discrete. The same is true for the topology ZG2 [x] . Theorem 1. For every infinite group G the 2-nd Zariski topology ZG2 [x] is not discrete. Proof. look up unicorn dresses