Notes on microstate free entropy of projections

A Note about proving non-$Γ$ under a finite non-microstates free Fisher information Assumption

We prove that if $X_{1},...,X_{n} (n >1)$ are selfadjoints in a $W^{*}$-probability space with finite non-microstates free Fisher information, then the von Neumann algebra $W^{*}(X_{1},...,X_{n})$ they generate doesn't have property $Γ$ (especially is not amenable). This is an analog of a well-known result of Voiculescu for microstates free entropy. We also prove factoriality under finite non-microstates entropy.

A note on "Weak limits of almost invariant projections"

We give alternative proofs to certain results in the paper "Weak limits of almost invariant projections" by using ultraproducts of operators.

Jordan格完备化及关于内射包络与von Neumann代数的注记

The Jordan lattice completion and a note on injective envelopes and von Neumann algebras

本文通过为函数系引入两种格构造，研究可分C*-代数的内射包络与包络von Neumann代数的关系，并刻画了由正投影上的取值决定投影映射的非线性映射。

关于平展广群代数中的投影与保对角同态的注记

A note on projections in étale groupoid algebras and diagonal preserving homomorphisms

本文刻画了满足“豪斯多夫充足广群代数的任意$\ast$-同态均自动保对角”性质的环，其恰好是Carlsen研究的复数共轭闭子环，且给出了比Leavitt路代数情形更简洁的广群层面证明。

A note on geodesics of projections in the Calkin algebra

Let ${\cal C}({\cal H})={\cal B}({\cal H}) / {\cal K}({\cal H})$ be the Calkin algebra (${\cal B}({\cal H})$ the algebra of bounded operators on the Hilbert space ${\cal H}$, ${\cal K}({\cal H})$ the ideal of compact operators and $π:{\cal B}({\cal H})\to {\cal C}({\cal H})$ the quotient map), and ${\cal P}_{{\cal C}({\cal H})}$ the differentiable manifold of selfadjoint projections in ${\cal C}({\cal H})$. A projection $p$ in ${\cal C}({\cal H})$ can be lifted to a projection $P\in{\cal B}({\cal H})$: $π(P)=p$. We show that given $p,q \in {\cal P}_{{\cal C}({\cal H})}$, there exists a minimal…

关于自由无散度向量场的注记

A note on free divergence-free vector fields

本文展示了全Fock空间上循环梯度与齐次自由无散度向量场的基，确定了Voiculescu自由无散度向量场的维数，并给出了相关正交投影的具体公式。