Zhaolin Yao

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math.OA2025

A local quantization principle for inclusions of tracial von Neumann algebras

Xinyan Cao, Junsheng Fang, Chunlan Jiang +1

We study the local quantization principle (after Sorin Popa~\cite{popa 94} and \cite{popa 95}) of inclusions of tracial von Neumann algebras. Let $(M, τ)$ be a type ${\rm…

math.OA2023

On Diximier's averaging theorem for operators in type $II_{1}$ factors

Shilin Wen, Junsheng Fang, Zhaolin Yao

Let $\M$ be a type $I I_{1}$ factor and let $τ$ be the faithful normal tracial state on $\M$. In this paper, we prove that given finite elements $X_1,\cdots X_n \in \M$, there i…

math.OA2020

On finite sums of projections and Dixmier's averaging theorem for type $II_{1}$ factors

Xinyan Cao, Junsheng Fang, Zhaolin Yao

Let $M$ be a type $I I_{1}$ factor and let $τ$ be the faithful normal tracial state on $M$ . In this paper, we prove that given an $X \in M$ , $X=X^*…

math.OA2020

Strong sums of projections in type $II$ factors

Xinyan Cao, Junsheng Fang, Zhaolin Yao

Let $M$ be a type $II$ factor and let $τ$ be the faithful positive semifinite normal trace, unique up to scalar multiples in the type $II_{\infty}$ case and normalized by…

A local quantization principle for inclusions of tracial von Neumann algebras

On Diximier's averaging theorem for operators in type II1​ factors

On finite sums of projections and Dixmier's averaging theorem for type II1​ factors

Strong sums of projections in type II factors

On Diximier's averaging theorem for operators in type $II_{1}$ factors

On finite sums of projections and Dixmier's averaging theorem for type $II_{1}$ factors

Strong sums of projections in type $II$ factors