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Non-Isomorphic Non-Hyperfinite Factors

Published online by Cambridge University Press:  20 November 2018

Wai-Mee Ching
Wai-Mee Ching*
Affiliation:
Louisiana State University, Baton Rouge, Louisiana; Courant Institute of Mathematical Sciences, New York, New York
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A von Neumann algebra is called hyperfinite if it is the weak closure of an increasing sequence of finite-dimensional von Neumann subalgebras. For a separable infinite-dimensional Hilbert space the following is known: there exist hyperfinite and non-hyperfinite factors of type II1 (4, Theorem 16’), and of type III (8, Theorem 1); all hyperfinite factors of type Hi are isomorphic (4, Theorem 14); there exist uncountably many non-isomorphic hyperfinite factors of type III (7, Theorem 4.8); there exist two nonisomorphic non-hyperfinite factors of type II1 (10), and of type III (11). In this paper we will show that on a separable infinite-dimensional Hilbert space there exist three non-isomorphic non-hyperfinite factors of type II1 (Theorem 2), and of type III (Theorem 3).

Section 1 contains an exposition of crossed product, which is developed mainly for the construction of factors of type III in § 3.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 1293 - 1308
Copyright
Copyright © Canadian Mathematical Society 1969

References

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