作为算子模的$C^*$-代数的内射包络

Injective Envelopes and Local Multiplier Algebras of Some Spatial Continuous Trace C*-Algebras

A precise description of the injective envelope of a spatial continuous trace C*-algebra A over a Stonean space Delta is given. The description is based on the notion of a weakly continuous Hilbert bundle, which we show to be a Kaplansky--Hilbert module over the abelian AW*-algebra C(Delta). We then use the description of the injective envelope of A to study the first- and second-order local multiplier algebras of A. In particular, we show that the second-order local multiplier algebra of A is precisely the injective envelope of A.

内射包范畴方法

A categorical approach to injective envelopes

探讨算子空间范畴间的函子及对象在内射性与内射包上的关系，比较内射性的范畴定义与算子理论定义，并附算子空间单位化及其内射包的讨论。

Weak Expectations and the Injective Envelope

Given a unital C*-subalgebra of B(H), we study the set of all possible images of its injective envelope that are contained in B(H) and their position relative to the double commutant of the algebra in order to obtain more information about the existence or non-existence of weak expectations. We study the subset of B(H) that is the intersection of all possible images of the injective envelope and show that it is simultaneously a reflexive cover and a new type of order completion of the algebra.

Injective envelopes and the intersection property

We consider the ideal structure of a reduced crossed product of a unital $C^*$-algebra equipped with an action of a discrete group. More specifically we find sufficient and necessary conditions for the group action to have the intersection property, meaning that non-zero ideals in the reduced crossed product restrict to non-zero ideals in the underlying $C^*$-algebra. We show that the intersection property of a group action on a $C^*$-algebra is equivalent to the intersection property of the action on the equivariant injective envelope. We also show that the centre of the equivariant injective…

局部C*-代数的可 Injective 包裹

Injective envelopes for locally C*-algebras

本文研究了局部C*-代数的可接受可 Injective 包裹，证明了其唯一性，并探讨了局部W*-代数与C*-代数之间的可 Injectivity 关系。

Real structure in operator spaces, injective envelopes and $G$-spaces

We present some more foundations for a theory of real structure in operator spaces and algebras, in particular concerning the real case of the theory of injectivity, and the injective, ternary, and $C^*$-envelope. We consider the interaction between these topics and the complexification. We also generalize many of these results to the setting of operator spaces and systems acted upon by a group.

$C^*$-simplicity and Ozawa conjecture for groupoid $C^*$-algebras, part I: injective envelopes

This paper studies injective envelopes of groupoid dynamical systems and the corresponding boundaries. Analogue to the group case, we associate a bundle of compact Hausdorff spaces to any (discrete) groupoid (the Hamana boundary of the groupoid). We study bundles of compact topological spaces equipped with an action of a groupoid. We show that any groupoid has a minimal boundary (the Furstenberg boundary of the groupoid). We prove that the Hamana and Furstenberg boundaries are the same, for (discrete) groupoids. We find the relation between the reduced crossed product of the $\G$-injective env…

C*-代数的内射包络与局部乘子代数

Injective envelopes and local multiplier algebras of C*-algebras

本文研究C*-代数的局部乘子代数与内射包络的关系，证明前者可嵌入后者、二者内射包络一致，并给出Wittstock型延拓定理成立当且仅当二者相等，且该问题等价于Kaplansky关于AW*-代数单调完备性的猜想。

实 C*-代数与 AW*-代数的内射包络

Injective envelopes of real C*- and AW*-algebras

本文研究实 C*-代数的内射包络，证明外 *-自同构可唯一延拓、单实 C*-代数的内射包络为单实 AW*-因子，并构造例子说明 III 型内射实 AW*-因子类比对应 W*-因子类至少多一个。

Purity of the Embeddings of Operator Systems into their C$^*$- and Injective Envelopes

We study the issue of issue of purity (as a completely positive linear map) for identity maps on operators systems and for their completely isometric embeddings into their C$^*$-envelopes and injective envelopes. Our most general result states that the canonical embedding of an operator system $\mathcal R$ into its injective envelope $\mathcal I(\mathcal R)$ is pure if and only if the C$^*$-envelope of $\mathcal R$ is a prime C$^*$-algebra. To prove this, we also show that the identity map on any AW$^*$-factor is a pure completely positive linear map. For embeddings of operator systems into th…

Maximal C*-algebras of quotients and injective envelopes of C*-algebras

A new C*-enlargement of a C*-algebra $A$ nested between the local multiplier algebra $M_{\text{loc}}(A)$ of $A$ and its injective envelope $I(A)$ is introduced. Various aspects of this maximal C*-algebra of quotients, $Q_{\text{max}}(A)$, are studied, notably in the setting of AW*-algebras. As a by-product we obtain a new example of a type I C*-algebra $A$ such that $M_{\text{loc}}(M_{\text{loc}}(A))\ne M_{\text{loc}}(A)$.

部分 C* - 动力系统的内射包

Injective envelopes of partial C*-dynamical systems

该研究将滨名内射包理论扩展到部分 C* - 动力系统领域，证明了系统与内射包理想交性质的关系，建立了系统内射包与其包络作用内射包间的联系，还表明对阿贝尔系统构造与相关函数代数一致，关键是考虑了广义系统概念。

关于内射包络与冯·诺伊曼代数的一个注记

A note on injective envelopes and von Neumann algebras

本文探讨了 C*-代数 A 的内射包络 I(A) 与其内射表示 lambda 生成的冯·诺伊曼代数之间的关系，证明了存在接近 *-同态的正收缩映射，其核为双边理想。

Hamana的注射包作为最大刚性乘法覆盖

Hamana's injective envelope as a maximal rigid multiplier cover

本文研究了在Hamana意义下刚性的乘法覆盖，证明Hamana注射包是最大刚性乘法覆盖，并揭示了其在序理论中的 characterization。

Injective and projective Hilbert C*-modules, and C*-algebras of compact operators

We consider projectivity and injectivity of Hilbert C*-modules in the categories of Hilbert C*-(bi-)modules over a fixed C*-algebra of coefficients (and another fixed C*-algebra represented as bounded module operators) and bounded (bi-)module morphisms, either necessarily adjointable or arbitrary ones. As a consequence of these investigations, we obtain a set of equivalent conditions characterizing C*-subalgebras of C*-algebras of compact operators on Hilbert spaces in terms of general properties of Hilbert C*-modules over them. Our results complement results recently obtained by B. Magajna, J…