We introduce Banach algebras arising from tensor norms. By these Banach algebras we make Arensregular Banach algebras such that tensor product becomes irregular, where is tensor norm. Weillustrate injective tensor product, does not preserve bounded approximate identity and it is notalgebra norm.

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...

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...