The Effros-Maréchal topology in the space of von Neumann algebras, II
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We continue our study [9] of the Effros-Maréchal topology on the space vN(H) of all von Neumann algebras acting on a fixed separable Hilbert space H. In particular, we prove that factors of each of the types: II1, II∞, and (for fixed λ∈[0, 1]) IIIλ, form a dense subset of vN(H). Moreover, the density of type I-factors (or, equivalently, of injective factors) in vN(H), is proved to be equivalent to famous conjectures by A. Connes and E. Kirchberg.
Originalsprog | Engelsk |
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Tidsskrift | Journal of Functional Analysis |
Vol/bind | 171 |
Udgave nummer | 2 |
Sider (fra-til) | 401-431 |
Antal sider | 31 |
ISSN | 0022-1236 |
DOI | |
Status | Udgivet - 10 mar. 2000 |
ID: 233652616