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...

Let S be a (discrete) semigroup, and let ` (S) be the Banach algebra which is the semigroup algebra of S. We shall study the structure of this Banach algebra and of its second dual. We shall determine exactly when ` (S) is amenable as a Banach algebra, and shall discuss its amenability constant, showing that there are ‘forbidden values’ for this constant. The second dual of ` (S) is the Banach ...

Let S be a semigroup, and let ` (S) be the Banach algebra which is the semigroup algebra of S. We shall study the structure of this Banach algebra and of its second dual. We shall determine exactly when ` (S) is amenable as a Banach algebra, and shall discuss its amenability constant, showing that there are ‘forbidden values’ for this constant. The second dual of ` (S) is the Banach algebraM(βS...

let  and  be banach algebras, ,  and . we define an -product on  which is a strongly splitting extension of  by . we show that these products form a large class of banach algebras which contains all module extensions and triangular banach algebras. then we consider spectrum, arens regularity, amenability and weak amenability of these products.

in this paper, we extend some propositions of banachalgebras into module actions and establish the relationships betweentopological centers of module actions. we introduce some newconcepts as                         -property and -property for banach modules and obtain some conclusions inthe topological center of module actions and arens regularity of banachalgebras.

‎let $v$ be a vector space over a field $f$ of characteristic $pgeq 0$ and let‎ ‎$t$ be a regular subgroup of the affine group $agl(v)$‎. ‎in the finite dimensional case we show that‎, ‎if $t$ is abelian or $p>0$‎, ‎then $t$ is unipotent‎. ‎for $t$ abelian‎, ‎pushing forward some ideas used in [a‎. ‎caranti‎, ‎f‎. ‎dalla volta and m‎. ‎sala‎, ‎abelian regular subgroups of the affine group and r...