A note on approximate amenability of type I von Neumann algebras
Yong Zhang
Abstract
Using the methods of Ozawa [4] and Runde [5], we show that a type I von Neumann algebra is approximately amenable if and only if it is amenable.
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A note on approximate amenability of type I von Neumann algebras
Authors
Abstract
Using the methods of Ozawa [4] and Runde [5], we show that a type I von Neumann algebra is approximately amenable if and only if it is amenable.
Paper Structure
This paper contains 5 theorems, 28 equations.
Key Result
Proposition 1
Let $\mathcal{M}$ be a type I von Neumann algebra of the form E: type I. If there is $N\in \mathbb{N}$ such that dim$(\mathcal{H}_\alpha) \leq N$ for all $\alpha$, then $\mathcal{M}$ is amenable.
Theorems & Definitions (6)
- Proposition 1
- Lemma 2
- Lemma 4: Lemma 3.4.5 of Runde
- Proposition 5
- Theorem 6
- Remark