A direct proof of Z-stability for AH algebras of bounded topological dimension

Aperiodicity Conditions in Topological $k$-Graphs

We give two new conditions on topological $k$-graphs that are equivalent to the Yeend's aperiodicity Condition (A). Each of the new conditions concerns finite paths rather than infinite. We use a specific example, resulting from a new construction of a twisted topological $k$-graph, to demonstrate the improvements achieved by the new conditions. Reducing this proof of equivalence to the discrete case also gives a new direct proof of the corresponding conditions in discrete $k$-graphs, where previous proofs depended on simplicity of the corresponding C$^*$-algebra.

Elementary Proofs of Grothendieck Theorems for Completely Bounded Norms

We provide alternative proofs of two recent Grothendieck theorems for jointly completely bounded bilinear forms, originally due to Pisier and Shlyakhtenko (Invent. Math. 2002) and Haagerup and Musat (Invent. Math. 2008). Our proofs are elementary and are inspired by the so-called embezzlement states in quantum information theory. Moreover, our proofs lead to quantitative estimates.

Unitarization of uniformly bounded subgroups in finite von Neumann algebras

This note will present a new proof of the fact that every uniformly bounded group of invertible elements in a finite von Neumann algebra is similar to a unitary group. The proof involves metric geometric arguments in the non-positively curved space of positive invertible operators of the algebra; in 1974 Vasilescu and Zsido proved this result using the Ryll-Nardzewsky fixed point theorem.

冯·诺依曼代数的一阶上同调消失性与强1有界性

Vanishing first cohomology and strong 1-boundedness for von Neumann algebras

本文简化证明了sofic有限表示群若一阶ℓ²-Betti数消失则其群冯·诺依曼代数是强1有界的，并给出性质T情形的简短证明。

On the Grothendieck Theorem for jointly completely bounded bilinear forms

We show how the proof of the Grothendieck Theorem for jointly completely bounded bilinear forms on C*-algebras by Haagerup and Musat can be modified in such a way that the method of proof is essentially C*-algebraic. To this purpose, we use Cuntz algebras rather than type III factors. Furthermore, we show that the best constant in Blecher's inequality is strictly greater than one.