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Rescalings of free products of II$_1$-factors

Author(s): Ken Dykema; Florin Radulescu
Journal: Proc. Amer. Math. Soc. 131 (2003), 1813-1816.
MSC (2000): Primary 46L09
Posted: October 1, 2002
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Abstract: We introduce the notation $\mathcal{Q}(1)*\cdots*\mathcal{Q}(n)*L(\mathbf F_r)$ for von Neumann algebra II$_1$-factors where $r$ is allowed to be negative. This notation is defined by rescalings of free products of II$_1$-factors, and is proved to be consistent with known results and natural operations. We also give two statements which we prove are equivalent to isomorphism of free group factors.

References:

1.
K. Dykema, Free products of hyperfinite von Neumann algebras and free dimension, Duke Math. J. 69 (1993), 97-119. MR 93m:46071

2.
, Interpolated free group factors, Pacific J. Math. 163 (1994), 123-135. MR 95c:46103

3.
, Free subproducts and free scaled products of II$_1$-factors, J. Funct. Anal. (to appear).

4.
K. Dykema, F. Radulescu, Compressions of free products of von Neumann algebras, Math. Ann. 316 (2000), 61-82. MR 2001f:46100

5.
F.J. Murray and J. von Neumann, Rings of operators. IV, Ann. of Math. 44 (1943), 716-808. MR 5:101a

6.
F. Radulescu, Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index, Invent. Math. 115 (1994), 347-389. MR 95c:46102

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Additional Information:

Ken Dykema
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843--3368
Email: Ken.Dykema@math.tamu.edu

Florin Radulescu
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242--1466
Email: radulesc@math.uiowa.edu

DOI: 10.1090/S0002-9939-02-06749-7
PII: S 0002-9939(02)06749-7
Received by editor(s): April 3, 2001
Received by editor(s) in revised form: January 18, 2002
Posted: October 1, 2002
Additional Notes: The first author was partially supported by NSF grant DMS--0070558
The second author was partially supported by NSF grant DMS--9970486. Both authors also thank the Mathematical Sciences Research Institute, where they were engaged in this work. Research at MSRI is supported in part by NSF grant DMS--9701755.
Communicated by: David R. Larson
Copyright of article: Copyright 2002, American Mathematical Society

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