The Effros-Maréchal topology in the space of von Neumann algebras

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Standard

The Effros-Maréchal topology in the space of von Neumann algebras. / Haagerup, Uffe; Winsløw, Carl.

I: American Journal of Mathematics, Bind 120, Nr. 3, 01.06.1998, s. 567-617.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Haagerup, U & Winsløw, C 1998, 'The Effros-Maréchal topology in the space of von Neumann algebras', American Journal of Mathematics, bind 120, nr. 3, s. 567-617.

APA

Haagerup, U., & Winsløw, C. (1998). The Effros-Maréchal topology in the space of von Neumann algebras. American Journal of Mathematics, 120(3), 567-617.

Vancouver

Haagerup U, Winsløw C. The Effros-Maréchal topology in the space of von Neumann algebras. American Journal of Mathematics. 1998 jun. 1;120(3):567-617.

Author

Haagerup, Uffe ; Winsløw, Carl. / The Effros-Maréchal topology in the space of von Neumann algebras. I: American Journal of Mathematics. 1998 ; Bind 120, Nr. 3. s. 567-617.

Bibtex

@article{37060b754e28413ab25fe4791c932a1b,
title = "The Effros-Mar{\'e}chal topology in the space of von Neumann algebras",
abstract = "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.",
author = "Uffe Haagerup and Carl Winsl{\o}w",
year = "1998",
month = jun,
day = "1",
language = "English",
volume = "120",
pages = "567--617",
journal = "American Journal of Mathematics",
issn = "0002-9327",
publisher = "TheJohns Hopkins University Press",
number = "3",

}

RIS

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