Completely bounded isomorphisms of operator algebras
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- by Alvaro Arias PDF
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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.
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$\{VN(F_{n}):n\geq 2\}$. The $II_{1}$ factors generated by the left regular representation of the free group on $n$-generators.
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$\{C_{\lambda }^{*}(F_{n}):n\geq 2\}$. The reduced $C^{*}$-algebras of the free group on $n$-generators.
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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
- MR Author ID: 27000
- Email: arias@ringer.cs.utsa.edu
- 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
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1091-1101
- MSC (1991): Primary 47D25; Secondary 46L89
- DOI: https://doi.org/10.1090/S0002-9939-96-03060-2
- MathSciNet review: 1301485