The free entropy dimension of hyperfinite von Neumann algebras

Author:
Kenley Jung

Journal:
Trans. Amer. Math. Soc. **355** (2003), 5053-5089

MSC (2000):
Primary 46L54; Secondary 52C17, 53C30

DOI:
https://doi.org/10.1090/S0002-9947-03-03286-0

Published electronically:
July 24, 2003

MathSciNet review:
1997595

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Abstract: Suppose is a hyperfinite von Neumann algebra with a normal, tracial state and is a set of selfadjoint generators for . We calculate , the modified free entropy dimension of . Moreover, we show that depends only on and . Consequently, is independent of the choice of generators for . In the course of the argument we show that if is a set of selfadjoint generators for a von Neumann algebra with a normal, tracial state and has finite-dimensional approximants, then for any hyperfinite von Neumann subalgebra of Combined with a result by Voiculescu, this implies that if has a regular diffuse hyperfinite von Neumann subalgebra, then .

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Additional Information

**Kenley Jung**

Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720-3840

Email:
factor@math.berkeley.edu

DOI:
https://doi.org/10.1090/S0002-9947-03-03286-0

Received by editor(s):
March 4, 2002

Received by editor(s) in revised form:
January 9, 2003

Published electronically:
July 24, 2003

Additional Notes:
Research supported in part by the NSF

Dedicated:
For my parents

Article copyright:
© Copyright 2003
American Mathematical Society