A remark on the minimal index of subgfactors
type: Item
instance of: scholarly article
title: A remark on the minimal index of subgfactors
zbMATH Open document ID: 0791.46040
DOI: 10.1016/0022-1236(92)90118-3
author: Hideki Kosaki
author: Roberto Longo
published in: Journal of Functional Analysis
publication date: 1992-09-27T00:00:00Z
review text: Let \(M\supset N\) be factors with a faithful normal conditional expectation \(E: M\to N\) satisfying \(\text{Ind } E<\infty\). Let \(N\subset M\subset M_ 1\subset M_ 2\subset\dots\) be the Jones tower of basic constructions, and \(E_ k: M_ k\to M_{k-1}\) be the dual expectation constructed canonically from \(E\). The authors prove tht, if \(E\) is minimal, then so is the composition \(E\circ E_ 1\circ \dots\circ E_ k: M_ k\to N\). To achieve this result, they use the tensoring by a factor of type \(\text{III}_ 1\) to reduce the problem to the \(\text{II}_ 1\) case so that \textit{M. Pimsner} and \textit{S. Popa's} result in Trans. Am. Math. Soc. 310, No. 1, 127-133 (1988; Zbl 0706.46047) can be applied.
Mathematics Subject Classification ID: 46L37
Mathematics Subject Classification ID: 46L10
zbMATH DE Number: 65351
zbMATH Keywords: index of subfactors
zbMATH Keywords: Jones basic construction
zbMATH Keywords: factors with a faithful normal conditional expectation
zbMATH Keywords: dual expectation
MaRDI profile type: Publication
full work available at URL: 0022-1236(92)90118-3
OpenAlex ID: W2110835917
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description: scientific article; zbMATH DE number 65351