Completely bounded isomorphisms of operator algebras

Author:
Alvaro Arias

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

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Abstract | References | Similar Articles | Additional Information

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.

- . The factors generated by the left regular representation of the free group on -generators.
- . The reduced -algebras of the free group on -generators.
- Some ``non-commutative'' analytic spaces introduced by G. Popescu in 1991.

**[AP]**A. Arias and G. Popescu,*Factorization and reflexivity on Fock spaces*, preprint.**[BP]**D. Blecher and V. Paulsen,*Tensor products of operator spaces*, J. Funct. Anal.**99**(1991), 262--292. MR**93d:46095****[CS]**E. Christensen and A. M. Sinclair,*Completely bounded isomorphisms of injective von Neumann algebras*, Proc. Edinburgh Math. Soc. (2)**32**(1989), 317--327. MR**90k:46135****[E]**E. Effros,*Advances in quantized functional analysis*, Proceedings of the International Congress of Math., Berkeley, 1986, pp. 906--916. MR**89e:46064****[ER]**E. Effros and Z. J. Ruan,*A new approach to operator spaces*, Canad. Math. Bull.**34**(1991), 329--337. MR**93a:47045****[FP]**A. Figa-Talamanca and M. Picardello,*Harmonic analysis of free groups*, Lecture notes in Pure and Applied Mathematics, vol. 87, Marcel Dekker, New York, 1983. MR**85j:43001****[HP]**U. Haagerup and G. Pisier,*Bounded linear operators between -algebras*, Duke Math. J.**71**(1993), 889--925. MR**94k:46112****[PV]**M. Pimsner and D. Voiculescu,*-groups of reduced crossed products by free groups*, J. Operator Theory**8**(1982), 131--156. MR**84d:46092****[P]**G. Pisier,*The operator Hilbert space , complex interpolation and tensor norms*, Mem. Amer. Math. Soc. (to appear). CMP**95:15****[Po]**G. Popescu,*von Neumann inequality for*, Math. Scand.**68**(1991), 292--304. MR**92k:47073****[RW]**A. G. Robertson and S. Wassermann,*Completely bounded isomorphisms of injective operator systems*, Bull. London Math. Soc.**21**(1989), 285--290. MR**90c:47077****[S]**S. Sakai,*-algebras and -algebras*, Springer-Verlag, New York, 1971. MR**56:1082**

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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

Email:
arias@ringer.cs.utsa.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03060-2

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