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Completely bounded isomorphisms of operator algebras

Author: Alvaro Arias
Journal: Proc. Amer. Math. Soc. 124 (1996), 1091-1101
MSC (1991): Primary 47D25; Secondary 46L89
MathSciNet review: 1301485
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Abstract: In this paper the author proves that any two elements from one of the following classes of operators are completely isomorphic to each other.

  1. $\{VN(F_{n}):n\geq 2\}$. The $II_{1}$ factors generated by the left regular representation of the free group on $n$-generators.
  2. $\{C_{\lambda }^{*}(F_{n}):n\geq 2\}$. The reduced $C^{*}$-algebras of the free group on $n$-generators.
  3. Some ``non-commutative'' analytic spaces introduced by G. Popescu in 1991.
The paper ends with some applications to Popescu's version of von Neumann's inequality.

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Additional Information

Alvaro Arias
Affiliation: Division of Mathematics and Statistics, The University of Texas at San Antonio, San Antonio, Texas 78249

Received by editor(s): February 21, 1994
Received by editor(s) in revised form: August 19, 1994
Additional Notes: Supported in part by NSF DMS 93-21369.
Communicated by: Dale Alspach
Article copyright: © Copyright 1996 American Mathematical Society