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Results tagged with banach-algebras
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user 25499
7
votes
1
answer
474
views
Projections in the tensor product of von Neumann algebras
This question seems elementary, but I have already asked an expert who does not know the answer, so I would like to post here.
Let $M$ and $N$ be von Neumann algebras, and let $M\bar{\otimes}N$ be th …
- 619
8
votes
Accepted
Projections in the tensor product of von Neumann algebras
The answer is no.
Proof. Let $\mathcal{H}$ and $\mathcal{K}$ be any infinite-dimensional Hilbert spaces, and let $\{\xi_n\}_{n=1}^\infty$ and $\{\eta_n\}_{n=1}^\infty$ be sequences of any orthogo …
- 619
7
votes
1
answer
427
views
Open projections and Murray-von Neumann equivalence
Let $\mathcal{A}$ be a $C^*$-algebra and $p\in\mathcal{A}^{**}$ be an open projection, that is, $p=p^*=p^2$ and $p\in\overline{(p\mathcal{A}^{**}p\cap\hat{\mathcal{A}})}^{\operatorname{w}^*}$, where $ …
- 619
2
votes
Accepted
Open projections and Murray-von Neumann equivalence
The answer is no.
Proof (Thomas Schick). The idea of the proof is due to Thomas Schick. I thank him for allowing me to reproduce it here. Let $\mathcal{A}:=C([0,1])\otimes\mathbb{M}_2$, where $\m …
- 619