Completely bounded isomorphisms of operator algebras

Arias, Alvaro

doi:10.1090/S0002-9939-96-03060-2

Completely bounded isomorphisms of operator algebras
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Proc. Amer. Math. Soc. 124 (1996), 1091-1101 Request permission

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.

$\{VN(F_{n}):n\geq 2\}$. The $II_{1}$ factors generated by the left regular representation of the free group on $n$-generators.
$\{C_{\lambda }^{*}(F_{n}):n\geq 2\}$. The reduced $C^{*}$-algebras of the free group on $n$-generators.
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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