On the properties of some sets of von Neumann algebras under perturbation

Autor:	LiGuang Wang
Rok vydání:	2014
Předmět:	Discrete mathematics Pure mathematics Fundamental group Mathematics::Operator Algebras General Mathematics Predual Separable space symbols.namesake Hausdorff distance Von Neumann algebra Operator algebra symbols Hyperfinite set Von Neumann architecture Mathematics
Zdroj:	Science China Mathematics. 58:1707-1714
ISSN:	1869-1862 1674-7283
DOI:	10.1007/s11425-014-4937-5
Popis:	Let ℒ be a type II1 factor with separable predual and τ be a normal faithful tracial state of ℒ. We first show that the set of subfactors of ℒ with property Γ, the set of type II1 subfactors of ℒ with similarity property and the set of all McDuff subfactors of ℒ are open and closed in the Hausdorff metric d 2 induced by the trace norm; then we show that the set of all hyperfinite von Neumann subalgebras of ℒ is closed in d 2. We also consider the connection of perturbation of operator algebras under d 2 with the fundamental group and the generator problem of type II1 factors. When is a finite von Neumann algebra with a normal faithful trace, the set of all von Neumann subalgebras of such that is rigid is closed in the Hausdorff metric d 2.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8f7c9ba4dc48049c827d35fd4363b70e https://doi.org/10.1007/s11425-014-4937-5 Zobrazit plný text záznamu Full text from SpringerLink