The Effros-Maréchal topology in the space of von Neumann algebras, II
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The Effros-Maréchal topology in the space of von Neumann algebras, II. / Haagerup, Uffe; Winsløw, Carl.
In: Journal of Functional Analysis, Vol. 171, No. 2, 10.03.2000, p. 401-431.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - The Effros-Maréchal topology in the space of von Neumann algebras, II
AU - Haagerup, Uffe
AU - Winsløw, Carl
PY - 2000/3/10
Y1 - 2000/3/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0034628713&partnerID=8YFLogxK
U2 - 10.1006/jfan.1999.3538
DO - 10.1006/jfan.1999.3538
M3 - Journal article
AN - SCOPUS:0034628713
VL - 171
SP - 401
EP - 431
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 2
ER -
ID: 233652616