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

• 论文 • 上一篇    下一篇

LINEAR ¤-DERIVATIONS ON JB¤-ALGEBRAS

Park Chun-Gil   


  1. 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).

LINEAR ¤-DERIVATIONS ON JB¤-ALGEBRAS

Park Chun-Gil   

  • Online:2005-07-20 Published:2005-07-20
  • Supported by:

    Supported by Korea Research Foundation (KRF-2004-041-C00023).

PDF (PC)

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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
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