套代数上的高阶全可导点

刘磊

数学学报 ›› 2015, Vol. 58 ›› Issue (5) : 861-870.

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数学学报 ›› 2015, Vol. 58 ›› Issue (5) : 861-870. DOI: 10.12386/A2015sxxb0086
论文

套代数上的高阶全可导点

    刘磊1,2
作者信息 +

Higher All-Derivable Points in Nest Algebras

    Lei LIU1,2
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文章历史 +

摘要

令N 是Hilbert空间H 上的非平凡完备套.若线性映射φ = {φ(n)}n∈N满足对任意n ∈ N以及S, T ∈ algN, 且ST = G, φ(n)(ST) = ∑i+j = nφ(i)(S)φj)(T), 则称φ为algN上的G点高阶可导映射.若G点高阶可导映射φ = {φ(n)}n∈N为高阶导子, 则称G为algN上的高阶全可导点. 本文证明了, G ∈ algN为高阶全可导点当且仅当G ≠ 0.

Abstract

Let N be a nontrivial complete nest on a Hilbert space H. We say that φ = {φ(n)}n∈N is a higher derivable linear mapping at G if φ(n)(ST) = ∑#em/em#+j=nφ(i)(S)φj(T) for all n ∈ N and S, T ∈ algN with ST = G. An element G ∈ algN is called a higher all-derivable point of algN if every higher derivable linear mapping φ = {φ(n)}n∈N at G is a higher derivation. In this paper, we show G ∈ algN is a higher all-derivable point if and only if G ≠ 0.

关键词

套代数 / 高阶导子 / 全可导点

Key words

nest algebras / higher derivations / all-derivable points

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刘磊. 套代数上的高阶全可导点. 数学学报, 2015, 58(5): 861-870 https://doi.org/10.12386/A2015sxxb0086
Lei LIU. Higher All-Derivable Points in Nest Algebras. Acta Mathematica Sinica, Chinese Series, 2015, 58(5): 861-870 https://doi.org/10.12386/A2015sxxb0086

参考文献

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基金

国家自然科学基金资助项目(11326109,11401452);中央高校基本科研业务费资助项目(JB140707)

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