查询词典 Jordan algebra

We show that Jordan multiplicative bijective maps on prime operator algebrasmust be additive. As its application, we show that every Jordan * multiplicative bijec-tive map on every factor C~* algebra is a C~* isomorphism or a conjugate C~* isomorphism,in the special case of B, it must be a *-isomorphism or a conjugate *-isomorphism.We also prove the additivity of Jordan multiplicative bijective maps on nest algebras.

证明了素算子代数上Jordan可乘双射的可加性，利用这一结论刻画了因子C~*代数上的Jordan*可乘双射，我们的结果表明这样的映射一定是C~*同构或共轭C~*同构；证明了套代数上的Jordan可乘双射的可加性。

As an application, we also describe the Jordan automorphisms of the algebra of upper triangular matrices over commutative rings, and give a sufficient and necessary condition for a commutative ring being connected.

作为应用，我们还刻划了交换环上的上三角矩阵代数的Jordan自同构，并给出了一个交换环是连通环的充要条件。

We prove that the Jordan semi-triple derivable maps of the algebra of all n×n matrices over a 2-torsion free commutative ring with unity is the sum of an inner derivation and A_φ, where A_φis the image of A underφapplied entrywise andφis an additive derivation over R.

证明了作用在一个包含单位元的可交换的2-无挠环上的矩阵代数上的拟三重Jordan可导映射是一个内导子与A_φ的和(这里A_φ是A在φ下逐点作用的像)。

In this paper,the concept of generalized Jordan derivable mappings at zero point on von Neumann algebra is introduced.The following conclusion is reached.

在文[4]中，朱军和熊昌萍引入了零点广义可导映射的概念，而导子与Jordan导子的关系十分密切。

In Chapter 2, we introduce a new scalar function of the vector optimization problem by virtue of the spectral function in Euclidean Jordan algebra. Correspondingly, we define the spectral scalar optimization problem and spectral scalar solution.

第二章借助欧几里德若当代数中谱函数的概念，引入了欧几里德若当代数向量优化新的标量函数——谱标量函数，并进一步定义了相应的谱标量优化问题及其谱标量解。

The generalized Jordan derivable mappings at zero point on von Neumann algebra are the sum of an inner derivation and identical mapping produced at a fixed operator,and the similar result is obtained on B.

受此启发，在本文中引入了零点广义Jordan可导映射的概念，并在此基础上对von Neumann代数上的

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。

Recalling some basic concepts and results on Euclidean Jordan algebra and vector optimization, we outline the contents studied in this thesis.

介绍了本文研究所需的基本概念和相关理论，继而提出了本文所要研究的主要内容。

Based on the speciality of the spectral function, we provide the sufficient conditions such that the spectral function are K—increasing (strictly K—increasing) in Euclidean Jordan algebra, and establish the relationship between the spectral scalar solution set and the K— efficient solution set of the Euclidean Jordan algebra vector optimization problem.

基于谱函数的特殊性，刻画了谱标量函数满足K-增性的充分条件，继而建立了谱标量解集与欧几里德若当代数向量优化问题K-弱有效解集和K-有效解集的包含关系。

In chapter 1, we introduce the notions of the approximately 2-local automorphisms, the approximately local Hilbert space representations and the approximately 2- local Hilbert space representations;We prove that every surjective and multiplicative approximately local *-automorphisms of a C*- algebra with a unique faithful tracial state is *-automorphisms;surjective approximately 2- local *- automorphisms of C*-algebra with unique faithful tracial states are Jordan *- automorphisms;Surjective approximately 2- local *- automorphisms of a finit factor are *-automorphisms;Approximately 2- local *- automorphisms of M_n are *-automorphisms.

第一章定义了近似2—局部自同构，近似局部表示，近似2—局部表示；证明了有唯一忠实迹态的C~*-代数上的满可乘近似局部*—自同构是*—自同构，满近似2—局部*—自同构是Jordan *—自同构，有限因子上的满近似2—局部*—自同构是*—自同构，以及矩阵代数M_n上的近似2—局部*—自同构是*—自同构。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失