In this paper, we study approximate identity properties, some propositions from Baker, Dales, Lau in general situations and establish relationships between the topological centers of module actions factorization properties with results group algebras. We consider under which sufficient necessary conditions Banach algebra $A\widehat{\otimes}B$ is Arens regular.

We study the worst-case error of quasi-Monte Carlo rules for multivariate integration in some weighted Sobolev spaces of functions defined on the product of d copies of the unit sphere Ss ⊆ Rs+1. The space is a tensor product of d reproducing kernel Hilbert spaces defined in terms of uniformly bounded ‘weight’ parameters γd,a for a = 1, 2, . . . , d. We prove that strong QMC tractability holds ...

We develop a Harder-Narasimhan theory for Kisin modules generalizing a similar theory for finite flat group schemes due to Fargues [Far10]. We prove the tensor product theorem, i.e., that the tensor product of semistable objects is again semi-stable. We then apply the tensor product theorem to the study of Kisin varieties for arbitrary connected reductive groups.

Under some assumptions we prove that the Deligne tensor product of categories of constructible perverse sheaves on pseudomanifolds X and Y is the category of constructible perverse sheaves on X × Y . The Deligne external tensor product functor is identified with the geometrical external tensor product.