2-$B(H)$上的局部导子与自同构

Conservative algebras of $2$-dimensional algebras, III

In the present paper we prove that every local and $2$-local derivation on conservative algebras of $2$-dimensional algebras are derivations. Also, we prove that every local and $2$-local automorphism on conservative algebras of $2$-dimensional algebras are automorphisms.

C* 代数上的紧量子群作用与不变导子

Compact quantum group actions on C*-algebras and invariant derivations

定义了C* 代数在紧量子群作用下的不变导子的概念，并证明了在一定条件下，这类导子是单参数自同构群的生成元.

运算型2-局部自同构/导子

Operational 2-local automorphisms/derivations

该研究针对标准算子代数上满足2-局部自同构类条件的映射，证明其或其负值为线性Jordan同态，并将类似结果推广到半有限von Neumann代数上的2-局部导子映射。

2-Local automorphisms on $AW^\ast$-algebras

The paper is devoted to 2-local automorphisms on $AW^\ast$-algebras. Using the technique of matrix algebras over a unital Banach algebra we prove that any 2-local automorphism on an arbitrary $AW^\ast$-algebra without finite type~I direct summands is a global automorphism.

算子代数的局部内自同构

Locally inner automorphisms of operator algebras

本文称有单位元的C* 代数的自同构是局部内自同构，如果它在任一元上与某个内自同构一致.本文对冯诺依曼代数的局部内性作了比较全面的研究，并与Haagerup-Stormer的点态内性作了比较。在某些von Neumann代数上，包括所有具有可分预对偶的代数，局部内自同构必是内自同构。但是transmitted递归构造证明了这在一般情况下是不正确的。作为应用，我们证明了单位C* 代数-代数的自同构轨道上的对角和下降到一个定义良好的映射当且仅当它的所有自同构都是局部内的。

希尔伯特空间上酉群与一般线性群的局部自同构

Local automorphisms of the unitary group and the general linear group on a Hilbert space

证明了复无限维可分希尔伯特空间上酉群或一般线性群的每一个2-局部自同构都是自同构。因此，这些类型的变换完全由它们在所讨论的群的两点子集上的局部作用决定。

局部乘子代数的内自同构与Connes谱

Automorphisms Inner in the Local Multiplier Algebra and Connes Spectrum

我们得到了不动点局部乘子代数的Connes谱与自同构的内性之间的关系。这些结果是Olesen，Pedersen和Stormer [6]，[7]，[9]以及Ara和Mathieu [1]中相应结果在局部乘子代数情形下的变形和/或推广.

An Atiyah Sequence for Noncommutative Principal Bundles

We present a derivation-based Atiyah sequence for noncommutative principal bundles. Along the way we treat the problem of deciding when a given $^*$-automorphism on the quantum base space lifts to a $^*$-automorphism on the quantum total space that commutes with the underlying structure group.

On 2-local *-automorphisms and 2-local isometries of B(H)

It is an important result of \v Semrl which states that every 2-local automorphism of the full operator algebra over a separable Hilbert space is necessarily an automorphism. In this paper we strengthen that result quite substantially for *-automorphisms. Indeed, we show that one can compress the defining two equations of 2-local *-automorphisms into one single equation, hence weakening the requirement significantly, but still keeping essentially the conclusion that such maps are necessarily *-automorphisms.

$2$-local automorphisms on finite-dimensional Lie algebras

We prove that every $2$-local automorphism on a finite-dimensional semi-simple Lie algebra $\mathcal{L}$ over an algebraically closed field of characteristic zero is an automorphism. We also show that each finite-dimensional nilpotent Lie algebra $\mathcal{L}$ with $\dim \mathcal{L}\geq 2$ admits a $2$-local automorphism which is not an automorphism.

关于紧群的群代数的局部自同构

On local automorphisms of group algebras of compact groups

证明了紧群$G$的群代数$L^p(G)$的局部等距自同构是等距自同构.

局部自同构算子理想上的乘法映射

Multiplicative maps on ideals of operators which are local automorphisms

本文给出了关于$C^*$ -代数B（H）的自同构群的自反性结果，H是可分的希尔伯特空间.设$ϕ:B(H)\to B(H)$是一个乘法映射（不假设线性或连续性），它在每一点都可以用算子范数中B（H）的自同构（当然，这些自同构可能依赖于点）来近似。则$ϕ$是代数B（H）的自同构.

巴拿赫空间上算子代数的局部自同构

Local automorphisms of operator algebras on Banach spaces

本文推广了Semrl的一个结果：可分无限维希尔伯特空间上的全算子代数的每一个2-局部自同构都是自同构.事实上，除了可分的希尔伯特空间，我们得到了同样的结论，为更大的类巴拿赫空间与Schauder基。证明依赖于一个类似的声明关于2-局部自同构的矩阵代数的声明，我们提出了一个简短的证明。需要得到这样的证明是制定塞姆尔的文件。

某些量子力学结构的局域自同构

Local automorphisms of some quantum mechanical structures

设H是可分的无限维复希尔伯特空间。证明了H上所有幂等元的偏序集（即偏序集）的每一个连续2-局部自同构都是自同构。在不作连续性假设的情况下，给出了关于H上所有投影的正交模偏序集和所有自伴算子的Jordan环的类似结果。