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LINEAR*-DERIVATIONS ON C*-ALGEBRASLINEAR*-DERIVATIONS ON C*-ALGEBRAS
- Other Titles
- LINEAR*-DERIVATIONS ON C*-ALGEBRAS
- Issue Date
- Mar-2010
- Publisher
- 충청수학회
- Keywords
- linear *-derivation; C*-algebra; functional equation; Hyers-Ulam-Rassias stability
- Citation
- 충청수학회지, v.23, no.1, pp 49 - 57
- Pages
- 9
- Indexed
- KCI
- Journal Title
- 충청수학회지
- Volume
- 23
- Number
- 1
- Start Page
- 49
- End Page
- 57
- ISSN
- 1226-3524
2383-6245
- Abstract
- It is shown that for a derivation ｆ(χ1 ··· χｊ-1χｊχｊ+1 ··· χk) = k∑ｊ=1 χ1 ··· χｊ-1χｊ+1 ···χkｆ(χｊ) on a unital C*-algebra Β, there exists a unique Ｃ-linear *-derivation Ｄ: Β→Β near the derivation, by using the Hyers-Ulam-Rassias stability of functional equations. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297--300.
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