Factor state extensions of type III

Robert Archbold, Aldo Lazar, Sze Kai Tsui, Stephen Wright

Research output: Contribution to journalArticlepeer-review

Abstract

Let B be a C*-subalgebra of A and θ{symbol} a factor state on B. Due to the independent work of S. Popa and R. Longo the existence of a factor state extension of θ{symbol} to A is assured in case of a separable B. However, the type of the extending factor state can't be determined according to their highly nonconstructive procedures. In this article we consider a type II1, factor state θ{symbol} on the Choi algebra embedded as a C*-subalgebra of the Cuntz algebra O2. Type IIIλ factor state extensions of θ{symbol} are constructed for λ = 1 and many λ's between 0 and 1.

Original languageEnglish
Pages (from-to)219-230
Number of pages12
JournalJournal of Functional Analysis
Volume95
Issue number1
DOIs
StatePublished - Jan 1991

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