In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on  a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of  level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity...

We prove that all Arens extensions of finite rank Riesz multimorphisms taking values in Archimedean spaces coincide and are multimorphisms. also that, for a class Banach lattices F, which includes F=c0,ℓp,c0(ℓp),ℓp(c0), ℓp(ℓs),1<p,s<∞, among many others, Aron-Berner any F-valued multimorphism between

This is a short comment on “The impacts of land plant evolution Earth's climate and oxygenation state – An interdisciplinary review” by Tais W. Dahl Susanne K.M. Arens, Chem. Geol. 547 (2020) Article 119665. We discuss what the sedimentary-stratigraphic record (SSR) can reveal about influence ancient plants erosion, demonstrate that intensive properties SSR are supportive hypotheses vegetation ...

Let L be a completely valued nonarchimedean field and g a finite dimensional Lie algebra over L. We show that its hyperenveloping algebra F(g) agrees with its Arens-Michael envelope and, furthermore, is a stably flat completion of its universal enveloping algebra. As an application, we prove that the Taylor relative cohomology for the locally convex algebra F(g) is naturally isomorphic to the L...

It was shown in papers of Dosi and a recent article the author that there is sheaf Frechet-Arens-Michael algebras (locally solvable complex case polynomial growth real) on character space nilpotent Lie algebra. For algebra group affine transformations line (the simplest non-nilpotent algebra) we construct analogous sheaves non-commutative smooth holomorphic functions special set representations.

The Arens-Michael functor in noncommutative geometry is an analogue of the analytification algebraic geometry: out ring “algebraic functions” on a affine scheme, it constructs “holomorphic when viewed as complex analytic space. In this paper, we explicitly compute envelopes Jordan plane and quantum enveloping algebra $U\_q(\mathfrak{sl}(2))$ $\mathfrak{sl}(2)$ for $|q|=1$.

A locally compact group G is discrete if and only the Fourier algebra A(G) has a non-zero (weakly) multiplier. We partially extend this result to setting of ultraspherical hypergroups. Let H be an hypergroup let A(H) denote corresponding algebra. will give several characterizations discreteness in terms algebraic properties A(H). also study Arens regularity closed ideals

1. R. F. Arens, A topology for spaces of transformations, Ann. of Math. vol. 47 (1946) pp. 480-495. 2. R. F. Arens ond J. L. Kelley, Characterizations of the space of continuous functions over a compact Hausdorff space, To be published in Trans. Amer. Math. Soc. 3. S. Banach, Théorie des opérations linéaires, Warsaw, 1932. 4. G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloquium Publications...