Singular extensions of the trace and the relative Dixmier property in the type 𝐼𝐼₁ factors

Author:

Pop Florin

Abstract

If N M N \subset M is an inclusion of type I I 1 \mathrm {II}_1 factors with N M = C I , N’\cap M = \mathbf {C} I, we study the connection between the existence of singular states on M M which extend the trace on N N and the Dixmier approximation property in M M with unitaries in N . N. We also prove the existence of singular conditional expectations from certain free product factors onto irreducible hyperfinite subfactors.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Irreducible inclusions of simple $C^*$-algebras;L’Enseignement Mathématique;2023-06-08

2. Relative Dixmier property and complete boundedness of modular maps;Mathematische Zeitschrift;2004-05-01

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