Amenability,tubularity, and embeddings into $$\mathcal{R}^{\omega}$$ |
| |
Authors: | Kenley Jung |
| |
Institution: | (1) Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA |
| |
Abstract: | Suppose M is a tracial von Neumann algebra embeddable into (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 and γ > 0 such that if then there exists a k × k unitary u satisfying 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 are conjugate by a unitary .
|
Research supported in part by the NSF.
Dedicated to Ed Effros on the occasion of his 70th birthday. |
| |
Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 46L54 Secondary 46L10 |
本文献已被 SpringerLink 等数据库收录! |
|