# Topologies on central extensions of von Neumann algebras

Shavkat Ayupov; Karimbergen Kudaybergenov; Rauaj Djumamuratov

Open Mathematics (2012)

- Volume: 10, Issue: 2, page 656-664
- ISSN: 2391-5455

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topShavkat Ayupov, Karimbergen Kudaybergenov, and Rauaj Djumamuratov. "Topologies on central extensions of von Neumann algebras." Open Mathematics 10.2 (2012): 656-664. <http://eudml.org/doc/269809>.

@article{ShavkatAyupov2012,

abstract = {Given a von Neumann algebra M, we consider the central extension E(M) of M. We introduce the topology t c(M) on E(M) generated by a center-valued norm and prove that it coincides with the topology of local convergence in measure on E(M) if and only if M does not have direct summands of type II. We also show that t c(M) restricted to the set E(M)h of self-adjoint elements of E(M) coincides with the order topology on E(M)h if and only if M is a σ-finite type Ifin von Neumann algebra.},

author = {Shavkat Ayupov, Karimbergen Kudaybergenov, Rauaj Djumamuratov},

journal = {Open Mathematics},

keywords = {von Neumann algebras; Central extensions; Local measure topology; central extensions; local measure topology},

language = {eng},

number = {2},

pages = {656-664},

title = {Topologies on central extensions of von Neumann algebras},

url = {http://eudml.org/doc/269809},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Shavkat Ayupov

AU - Karimbergen Kudaybergenov

AU - Rauaj Djumamuratov

TI - Topologies on central extensions of von Neumann algebras

JO - Open Mathematics

PY - 2012

VL - 10

IS - 2

SP - 656

EP - 664

AB - Given a von Neumann algebra M, we consider the central extension E(M) of M. We introduce the topology t c(M) on E(M) generated by a center-valued norm and prove that it coincides with the topology of local convergence in measure on E(M) if and only if M does not have direct summands of type II. We also show that t c(M) restricted to the set E(M)h of self-adjoint elements of E(M) coincides with the order topology on E(M)h if and only if M is a σ-finite type Ifin von Neumann algebra.

LA - eng

KW - von Neumann algebras; Central extensions; Local measure topology; central extensions; local measure topology

UR - http://eudml.org/doc/269809

ER -

## References

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