We prove that every nondegenerate Banach space representation of the Drinfeld–Jimbo algebra Uq(g) a semisimple complex Lie g is finite dimensional when |q|≠1. As corollary, we find an explicit form Arens–Michael envelope Uq(g), which similar to U(g) obtained by Joseph Taylor in 1970s. In case g=sl2, also consider theory corresponding analytic form, U˜(sl2)ℏ (with eℏ=q) and show it simpler than ...

The aim of this paper is to exploit the structure strongly continuous operator semigroups in order formulate a categorical framework which fresh perspective can be applied past theoretic results. In particular, we investigate inverse-producing Arens extension for Banach algebras (Trans. Am. Math. Soc. 88:536–548, 1958) adapted operators and by Batty Geyer (J. Oper. Theory 78(2):473–500, 2017) n...

in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.

We give lower bounds on the largest singular value of arbitrary matrices, some of which are asymptotically tight for almost all matrices. To study when these bounds are exact, we introduce several combinatorial concepts. In particular, we introduce regular, pseudo-regular, and almost regular matrices. Nonnegative, symmetric, almost regular matrices were studied earlier by Ho¤man, Wolfe, and Ho¤...