arens regularity and derivations of hilbert modules with the certain product
Authors
abstract
let $a$ be a $c^*$-algebra and $e$ be a left hilbert $a$-module. in this paper we define a product on $e$ that making it into a banach algebra and show that under the certain conditions $e$ is arens regular. we also study the relationship between derivations of $a$ and $e$.
similar resources
Arens regularity and derivations of Hilbert modules with the certain product
Let $A$ be a $C^*$-algebra and $E$ be a left Hilbert $A$-module. In this paper we define a product on $E$ that making it into a Banach algebra and show that under the certain conditions $E$ is Arens regular. We also study the relationship between derivations of $A$ and $E$.
full textArens Regularity and Weak Amenability of Certain Matrix Algebras
Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...
full textArens regularity of bilinear maps and Banach modules actions
Let $X$, $Y$ and $Z$ be Banach spaces and $f:Xtimes Y longrightarrow Z$ a bounded bilinear map. In this paper we study the relation between Arens regularity of $f$ and the reflexivity of $Y$. We also give some conditions under which the Arens regularity of a Banach algebra $A$ implies the Arens regularity of certain Banach right module action of $A$ .
full textarens regularity of bilinear maps and banach modules actions
let $x$, $y$ and $z$ be banach spaces and $f:xtimes y longrightarrow z$ a bounded bilinear map. in this paper we study the relation between arens regularity of $f$ and the reflexivity of $y$. we also give some conditions under which the arens regularity of a banach algebra $a$ implies the arens regularity of certain banach right module action of $a$ .
full textarens regularity and weak amenability of certain matrix algebras
motivated by an arens regularity problem, we introduce the concepts of matrix banach space and matrix banach algebra. the notion of matrix normed space in the sense of ruan is a special case of our matrix normed system. a matrix banach algebra is a matrix banach space with a completely contractive multiplication. we study the structure of matrix banach spaces and matrix banach algebras. then we...
full textNon Commutative Arens Algebras and Their Derivations
Given a von Neumann algebra M with a faithful normal semi-finite trace τ, we consider the non commutative Arens algebra Lω(M, τ) = ⋂ p≥1 Lp(M, τ) and the related algebras L2 (M, τ) = ⋂ p≥2 Lp(M, τ) and M + L2 (M, τ) which are proved to be complete metrizable locally convex *-algebras. The main purpose of the present paper is to prove that any derivation of the algebra M + L2 (M, τ) is inner and...
full textMy Resources
Save resource for easier access later
Journal title:
journal of algebra and related topicsPublisher: university of guilan
ISSN 2345-3931
volume 1
issue 1 2013
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023