On homomorphisms between $C^*$-algebras and linear derivations on $C^*$-algebras

Title:

On homomorphisms between $C^*$-algebras and linear derivations on $C^*$-algebras

Creator:

Park, Chun-Gil , Chu, Hahng-Yun , Park, Won-Gil , and Wee, Hee-Jeong

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:596748d0-f463-4178-a01f-95cf1ba39c2b
uuid:596748d0-f463-4178-a01f-95cf1ba39c2b

Subject:

$C^*$-algebra homomorphism, $C^*$-algebra, real rank zero, $\mathbb{C}$-linear $*$-derivation, and stability

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

It is shown that every almost linear Pexider mappings $f$, $g$, $h$ from a unital $C^*$-algebra $\mathcal A$ into a unital $C^*$-algebra $\mathcal B$ are homomorphisms when $f(2^n uy)=f(2^n u)f(y)$, $g(2^n uy)=g(2^nu)g(y)$ and $h(2^n uy)=h(2^n u)h(y)$ hold for all unitaries $u \in \mathcal A$, all $y \in \mathcal A$, and all $n\in \mathbb{Z}$, and that every almost linear continuous Pexider mappings $f$, $g$, $h$ from a unital $C^*$-algebra $\mathcal A$ of real rank zero into a unital $C^*$-algebra $\mathcal B$ are homomorphisms when $f(2^n uy)=f(2^n u)f(y)$, $g(2^n uy)=g(2^n u)g(y)$ and $h(2^n uy)=h(2^n u)h(y)$ hold for all $u \in \lbrace v\in \mathcal A\mid v=v^*\hspace{5.0pt}\text{and}\hspace{5.0pt}v\hspace{5.0pt}\text{is} \text{invertible}\rbrace $, all $y\in \mathcal A$ and all $n\in \mathbb{Z}$. Furthermore, we prove the Cauchy-Rassias stability of $*$-homomorphisms between unital $C^*$-algebras, and $\mathbb{C}$-linear $*$-derivations on unital $C^*$-algebras.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1055-1065

Source:

Czechoslovak Mathematical Journal | 2005 Volume:55 | Number:4

Harvested from:

CDK

Metadata only:

false