The relation $$xy-yx=h(y)$$ , where $$h$$ is a holomorphic function, occurs naturally in the definitions of some quantum groups. To attach rigorous meaning to right-hand side this equality, we assume that $$x$$ and $$y$$ are elements Banach algebra (or an Arens–Michael algebra). We prove universal generated by commutation kind can be represented explicitly as analytic Ore extension. An analysis...

Let G be a locally compact group. We shall study the Banach algebras which are the group algebra L(G) and the measure algebra M(G) on G, concentrating on their second dual algebras. As a preliminary we shall study the second dual C0(Ω) ′′ of the C∗-algebra C0(Ω) for a locally compact space Ω, recognizing this space as C(Ω̃), where Ω̃ is the hyper-Stonean envelope of Ω. We shall study the C∗-algeb...

Let $fM(X)$ be the  space of  all finite regular Borel measures on $X$. A general measure algebra is a subspace  of$fM(X)$,which is an $L$-space and has a multiplication preserving the probability measures. Let $cLsubseteqfM(X)$ be a general measure algebra on a locallycompact space $X$. In this paper, we investigate the relation between Arensregularity of $cL$ and the topology of $X$. We  find...

The paper is devoted to isometric Banach-space-theoretical structure of transportation cost (TC) spaces on finite metric spaces. TC are also known as Arens-Eells, Lipschitz-free, or Wasserstein A new notion a roadmap pertinent problem space has been introduced and used simplify proofs for the results representation quotients $$\ell _1$$ edge set over cycle space. Tolstoi-type theorem roadmaps p...