LINEAR ¤-DERIVATIONS ON JB¤-ALGEBRAS

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LINEAR ¤-DERIVATIONS ON JB¤-ALGEBRAS

LINEAR ¤-DERIVATIONS ON JB¤-ALGEBRAS

LINEAR ¤-DERIVATIONS ON JB¤-ALGEBRAS

LINEAR ¤-DERIVATIONS ON JB¤-ALGEBRAS

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数学物理学报(英文版) ›› 2005, Vol. 25 ›› Issue (3): 449-454.

Park Chun-Gil

Department of Mathematics, Chungnam National University, Daejeon 305-764, South Korea

出版日期:2005-07-20 发布日期:2005-07-20
基金资助:
Supported by Korea Research Foundation (KRF-2004-041-C00023).

Park Chun-Gil

Online:2005-07-20 Published:2005-07-20
Supported by:
Supported by Korea Research Foundation (KRF-2004-041-C00023).

摘要：

It is shown that for a derivation

$f(x_1 \circ \cdots \circ x_{j-1}\circ x_j\circ x_{j+1} \circ \cdots \circ x_k)= \sum_{j=1}^k x_1\circ \cdots \circ x_{j-1}\circ x_{j+1}\circ \cdots\circ x_k \circ f(x_j)$ on a

$JB^*$ -algebra

${\cal B}$ , there
exists a unique

${\Bbb C}$ -linear

$*$ -derivation

$D : {\cal B} \rightarrow {\cal B}$ near the derivation.

Abstract:

It is shown that for a derivation

$f(x_1 \circ \cdots \circ x_{j-1}\circ x_j\circ x_{j+1} \circ \cdots \circ x_k)= \sum_{j=1}^k x_1\circ \cdots \circ x_{j-1}\circ x_{j+1}\circ \cdots\circ x_k \circ f(x_j)$ on a

$JB^*$ -algebra

${\cal B}$ , there
exists a unique

${\Bbb C}$ -linear

$*$ -derivation

$D : {\cal B} \rightarrow {\cal B}$ near the derivation.

Key words: linear ¤-derivation, JB¤-algebra, functional equation, stability

中图分类号:

46K70

Park Chun-Gil. LINEAR ¤-DERIVATIONS ON JB¤-ALGEBRAS[J]. 数学物理学报(英文版), 2005, 25(3): 449-454.

Park Chun-Gil. LINEAR ¤-DERIVATIONS ON JB¤-ALGEBRAS[J]. Acta mathematica scientia,Series B, 2005, 25(3): 449-454.

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