# Some additive mappings on Banach ${\ast}$-algebras with derivations

Volume 11, Issue 3, pp 335--341 Publication Date: February 09, 2018
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### Authors

Jae-Hyeong Bae - Humanitas College, Kyung Hee University, Yongin 17104, Republic of Korea
Ick-Soon Chang - Department of Mathematics, Chungnam National University, 99 Daehangno, Yuseong-gu, Daejeon 34134, Republic of Korea

### Abstract

We take into account some additive mappings in Banach $\ast$-algebras with derivations. We will first study the conditions for additive mappings with derivations on Banach $\ast$-algebras. Then we prove some theorems involving linear mappings on Banach $\ast$-algebras with derivations. So derivations on $C^{\ast}$-algebra are characterized.

### Keywords

• Banach $\ast$-algebra
• $C^{\ast}$-algebra
• derivation

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