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

Park, Chun-Gil, et al. "On homomorphisms between $C^*$-algebras and linear derivations on $C^*$-algebras." Czechoslovak Mathematical Journal 55.4 (2005): 1055-1065. <http://eudml.org/doc/31009>.

@article{Park2005,
abstract = {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.},
author = {Park, Chun-Gil, Chu, Hahng-Yun, Park, Won-Gil, Wee, Hee-Jeong},
journal = {Czechoslovak Mathematical Journal},
keywords = {$C^*$-algebra homomorphism; $C^*$-algebra; real rank zero; $\mathbb \{C\}$-linear $*$-derivation; stability; -algebra homomorphism; -algebra; real rank zero; -linear -derivation; stability},
language = {eng},
number = {4},
pages = {1055-1065},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On homomorphisms between $C^*$-algebras and linear derivations on $C^*$-algebras},
url = {http://eudml.org/doc/31009},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Park, Chun-Gil
AU - Chu, Hahng-Yun
AU - Park, Won-Gil
AU - Wee, Hee-Jeong
TI - On homomorphisms between $C^*$-algebras and linear derivations on $C^*$-algebras
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 4
SP - 1055
EP - 1065
AB - 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.
LA - eng
KW - $C^*$-algebra homomorphism; $C^*$-algebra; real rank zero; $\mathbb {C}$-linear $*$-derivation; stability; -algebra homomorphism; -algebra; real rank zero; -linear -derivation; stability
UR - http://eudml.org/doc/31009
ER -