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Rescalings of free products of II -factors
Author(s):
Ken
Dykema;
Florin
Radulescu
Journal:
Proc. Amer. Math. Soc.
131
(2003),
1813-1816.
MSC (2000):
Primary 46L09
Posted:
October 1, 2002
MathSciNet review:
1955269
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Abstract:
We introduce the notation  for von Neumann algebra II -factors where  is allowed to be negative. This notation is defined by rescalings of free products of II -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
 -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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