Rank-one operators in reflexive one-sided A-submodules

关于希尔伯特C*-模本质和拓扑本质子模的研究

On Essential and Topologically Essential Submodules of Hilbert C*-Modules

本文研究了希尔伯特C*-模闭子模的两种大规模性概念：本质性和拓扑本质性，证明了闭右理想中这两种概念等价，并扩展至希尔伯特C*-模的闭子模。

关于 Hilbert C*-模中的大子模

On large submodules in Hilbert C*-modules

本文研究了C*-代数单边理想及Hilbert C*-模子模的多种“大”概念，证明其互不等价，并探讨了它们的关系、保持性质及利用本质右理想扩展内积。

The norm closed triple semigroup algebra

The w*-closed triple semigroup algebra was introduced by Power and the author in [19], where it was proved to be reflexive and to be chiral, in the sense of not being unitarily equivalent to its adjoint algebra. Here an analogous operator norm-closed triple semigroup algebra $A_{ph}^{G+}$ is considered and shown to be a triple semi-crossed product for the action on analytic almost periodic functions by the semigroups of one-sided translations and one-sided dilations. The structure of isometric automorphisms of $A_{ph}^{G+}$ is determined and $A_{ph}^{G+}$ is shown to be chiral with respect to …

Local maps and the representation theory of operator algebras

Using representation theory techniques we prove that various spaces of derivations or one-sided multipliers over certain operator algebras are reflexive. A sample result: any bounded local derivation (local left multiplier) on an automorphic semicrossed product is a derivation (resp. left multiplier). In the process we obtain various results of independent interest. In particular, the finite dimensional nest representations of the tensor algebra of a topological graph separate points.

保持Hilbert C*-模块的C*-子模映射

C*-submodule preserving module mappings on Hilbert C*-modules

研究Hilbert C*-模块上保持C*-子模的有界模映射的结构，证明其形式为d·id_X，其中d为可逆元素。

Rosenthal's theorem for subspaces of noncommutative Lp

We show that a reflexive subspace of the predual of a von Neumann algebra embeds into a noncommutative Lp space for some p>1. This is a noncommutative version of Rosenthal's result for commutative Lp spaces. Similarly for 1 < q < 2, an infinite dimensional subspace X of a noncommutative Lq space either contains lq or embeds in Lp for some q < p < 2. The novelty in the noncommutative setting is a double sided change of density.