derivations

derivations的基本解释

n.

发展( derivation的名词复数 ), 起源, 派生, 词源

与derivations相关的网络例句 [注：此内容来源于网络，仅供参考]

In this paper, we mainly disscuss derivable mappings at zero point, Jordan derivations and 2-local derivations on some operator algebras. The details as following:In chapter 1, some notations, definitions are introduced and some theorems are given.

本文主要对几类算子代数上的在零点可导映射和Jordan导子以及2-局部导子进行了研究，具体内容如下：第一章主要介绍了本文中要用到的一些符号，定义以及本文要用到的一些已知结论和定理。

In chapter 3, Jordan derivations and Jordan isomorphisms of nest algebras are investigated. It is proved that every Jordan derivation of nest algebra is an inner derivation. Every Jordan isomorphism between nest algebras is either an isomorphism or an anti-isomorphism. Finally, a norm estimate for derivations of nest subalgebras of von Neumann algebras is given, and it is shown that every nest subalgebra of factor von Neumann algebras has property AIP .

第三章研究了套代数上的Jordan导子和Jordan同构，证明了套代数上的每一个Jordan导子都是内导子；套代数之间的每一个Jordan同构要么是同构要么是反同构；最后给出了因子von Neumann代数中套子代数上导子的一个范数估计，同时也证明了因子von Neumann代数中的任何一个套子代数都具有AIP性质。

It is proved that every Lie derivation of nest algebra is the sum of an associative derivation and a general trace. Every Lie isomorphism between nest subalgebras of a factor von Neumann algebra is the sum of an isomorphism and a general trace or the sum of a negative anti-isomorphism and a general trace. Lie invariant subspace of linear mappings on Banach algebras is introduced, and linear maps from nest subalgebra of a factor von Neumann algebra into itself which satisfy the property that the space of derivations is their Lie invariant subspaces are characterized. Simultaneously, it is shown that such maps are Lie derivations modulo the set of scalar multiple of the identity.

得到Lie导子的特征表示，即套代数上的任何一个Lie导子都是内导子与广义迹之和；给出了Lie同构和同构及反同构之间的关系，即因子von Neumann代数中套子代数之间的任何一个Lie同构要么是同构与广义迹之和要么是负反同构与广义迹之和；引入了Banach代数上线性映射的Lie不变子空间，并给出von Neumann代数中套子代数上以导子空间为Lie不变子空间的线性映射的一个刻画，同时也表明在模去数乘恒等映射的意义下，以导子空间为Lie不变子空间的线性映射就是Lie导子。