The Effros-Maréchal topology in the space of von Neumann algebras
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The Effros-Maréchal topology in the space of von Neumann algebras. / Haagerup, Uffe; Winsløw, Carl.
In: American Journal of Mathematics, Vol. 120, No. 3, 01.06.1998, p. 567-617.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
AU - Haagerup, Uffe
AU - Winsløw, Carl
PY - 1998/6/1
Y1 - 1998/6/1
N2 - New concepts of limes inferior and limes superior in the space of von Neumann algebras on a fixed Hilbert space are defined, and the topology corresponding to these notions is related to earlier works of Effros and Marechal. A main technical result is that the commutant operation is a homeomorphism on the space of von Neumann algebras with this topology. Further, the topological properties of several classes and types of von Neumann factors (regarded as subspaces) are determined, and also continuity-type results for Tomita-Takesaki theory are proved. Some applications to subfactor theory are given.
AB - New concepts of limes inferior and limes superior in the space of von Neumann algebras on a fixed Hilbert space are defined, and the topology corresponding to these notions is related to earlier works of Effros and Marechal. A main technical result is that the commutant operation is a homeomorphism on the space of von Neumann algebras with this topology. Further, the topological properties of several classes and types of von Neumann factors (regarded as subspaces) are determined, and also continuity-type results for Tomita-Takesaki theory are proved. Some applications to subfactor theory are given.
UR - http://www.scopus.com/inward/record.url?scp=0002099669&partnerID=8YFLogxK
M3 - Journal article
AN - SCOPUS:0002099669
VL - 120
SP - 567
EP - 617
JO - American Journal of Mathematics
JF - American Journal of Mathematics
SN - 0002-9327
IS - 3
ER -
ID: 233652539