双重导子是导子的一种推广形式.令δ和ε为复线性代数A到自身内的两个映射, 称A到自身内的线性映射d是一个(δ, ε)-双重导子, 如果对任意a, b ∈ A, 有d(ab) = d(a)b+ad(b)+δ(a)ε(b)+ε(a)δ(b)成立.本文研究Banach代数上双重导子的自动连续性问题, 证明如果δ和ε为含单位元C*-代数上的两个在0点连续的映射, 则该C*-代数上的每个(δ, ε)-双重导子都是自动连续的.
Abstract
The double derivations are the generalized forms of ordinary derivations. For two mappings δ and ε from a complex linear algebra A into itself, a linear mapping d from A into itself is called a (δ, ε)-double derivation, if d(ab) = d(a)b+ad(b)+δ(a)ε(b)+ ε(a)δ(b) for all a, b ∈ A. We studies the problem on the automatic continuity of double derivations of Banach algebras. We prove that, if δ and ε are two continuous at zero mappings from a unital C*-algebra A into itself, then every (δ, ε)-double derivation of A is automatically continuous.
关键词
(&delta /
/
&epsilon /
-双重导子 /
自动连续性 /
Banach代数 /
C*-代数 /
*-映射
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Key words
(δ, ε-double derivation /
automatic continuity /
Banach algebra /
C*-algebra /
*-mapping
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参考文献
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脚注
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基金
国家自然科学基金资助项目(11271224,11371222)
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