Index of faithful normal conditional expectations

Author:
Sze-Kai Tsui

Journal:
Proc. Amer. Math. Soc. **111** (1991), 111-118

MSC:
Primary 46L37; Secondary 46L10, 46L35

DOI:
https://doi.org/10.1090/S0002-9939-1991-1033962-7

MathSciNet review:
1033962

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Abstract: Let be a faithful normal conditional expectation of a factor onto its subfactor , and the index of be denoted by . We investigate the question: For two such faithful normal conditional expectations of onto , when does hold? In this paper we answer this question completely for type factor . We also derive a tensor product formula for index, i.e., . For any we construct uncountable nonisomorphic faithful normal conditional expectations of a factor onto its subfactor with such that both of and , are of type or or . For each we exhibit a type factor and its subfactor and a faithful normal conditional expectation such that .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1033962-7

Keywords:
Index of faithful normal conditional expectations,
index of tensor products,
spatial derivatives,
relative commutants

Article copyright:
© Copyright 1991
American Mathematical Society