Amenability, tubularity, and embeddings into $$\mathcal{R}^{\omega}$$
Amenability, tubularity, and embeddings into $$\mathcal{R}^{\omega}$$
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顺应性、管状性和嵌入 $$mathcal{R}^{omega}$$
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发表时间：
2005
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通讯作者：
Kenley Jung
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文献类型：
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作者：
Kenley Jung
AbstractSuppose M is a tracial von Neumann algebra embeddable into $$\mathcal{R}^{\omega}$$ (the ultraproduct of the hyperfinite II1-factor) and X is an n-tuple of selfadjoint generators for M. Denote by Γ(X; m, k, γ) the microstate space of X of order (m, k ,γ). We say that X is tubular if for any ε > 0 there exist $$m \in \mathbb{N}$$ and γ > 0 such that if $$(x_{1},\ldots, x_{n}), (y_{1}, \ldots, y_{n}) \in \Gamma(X;m,k,\gamma),$$ then there exists a k × k unitary u satisfying $$|ux_iu^* - y_i|_2 < \epsilon$$ for each 1 ≤ i ≤ n. We show that the following conditions are equivalent:
M is amenable (i.e., injective).X is tubular.Any two embeddings of M into $$\mathcal{R}^{\omega}$$ are conjugate by a unitary $$u \in \mathcal {R}^{\omega}$$.
AbstractSuppose M is a tracial von Neumann algebra embeddable into $$\mathcal{R}^{\omega}$$ (the ultraproduct of the hyperfinite II1-factor) and X is an n-tuple of selfadjoint generators for M. Denote by Γ(X; m, k, γ) the microstate space of X of order (m, k ,γ). We say that X is tubular if for any ε > 0 there exist $$m \in \mathbb{N}$$ and γ > 0 such that if $$(x_{1},\ldots, x_{n}), (y_{1}, \ldots, y_{n}) \in \Gamma(X;m,k,\gamma),$$ then there exists a k × k unitary u satisfying $$|ux_iu^* - y_i|_2 < \epsilon$$ for each 1 ≤ i ≤ n. We show that the following conditions are equivalent:
M is amenable (i.e., injective).X is tubular.Any two embeddings of M into $$\mathcal{R}^{\omega}$$ are conjugate by a unitary $$u \in \mathcal {R}^{\omega}$$.