Regular normed bimodules

Derivations with values in quasi-normed bimodules of locally measurable operators

We prove that every derivation acting on a von Neumann algebra $\mathcal{M}$ with values in a quasi-normed bimodule of locally measurable operators affiliated with $\mathcal{M}$ is necessarily inner.

Representable bimodules over C*-algebras

Given two C*-algebras A and B, abstract A-B bimodules that can be isometrically represented as operator bimodules are characterised in terms of their norm. Various properties of such bimodules are given. Their theory is very similar to those of classical normed spaces.

Bimodules in crossed products and regular inclusions of finite factors

In this paper, we study bimodules over a von Neumann algebra $M$ in two related contexts. The first is an inclusion $M \subseteq M \rtimes_αG$, where $G$ is a discrete group acting on a factor $M$ by outer automorphisms. The second is a regular inclusion $M \subseteq N$ of finite factors. In the case of crossed products, we characterize the $M$-bimodules $X$ that lie between $M$ and $M \rtimes_αG$ and are closed in the Bures topology, in terms of the subsets of $G$. We show that this characterization also holds for $w^*$-closed bimodules when $G$ has the approximation property ($AP$), a class …

Toeplitz Matrices acting on the $\ell^2$-space of an imprimitivity bimodule

We give a definition of Toeplitz matrix acting on the $\ell^2$-space of an imprimitivity bimodule $X$ over a $C^*$-algebra $A$. We characterize the set of Toeplitz matrices as the closure in a certain topology of the image of the left regular representation of the crossed product $A\rtimes X$.

Gabor系统的Bessel对偶性：一个von Neumann代数视角

Bessel duality of Gabor systems: A von Neumann algebraic perspective

本文从von Neumann代数双模理论出发，证明正则Gabor系统的Bessel对偶性可由左右有界向量重合定理推导得出。

饱和Fell丛的谱几何

Spectral geometry of saturated Fell bundles

本文针对可数离散群上带谱三元组的饱和Fell丛，给出将其谱三元组提升至约化截面C*-代数的充分条件，结合纤维Dirac算子与长度算子构造提升后的谱三元组，还建立了可和性与稳定性判据，通过多类示例说明构造的适用范围。