|
Cuntz-Pimnser algebras, completely positive maps and Morita equivalence
Author(s):
Alberto
E.
Marrero;
Paul
S.
Muhly
Journal:
Proc. Amer. Math. Soc.
134
(2006),
1133-1135.
MSC (2000):
Primary 46L07, 46L08, 46M18, 47L30
Posted:
August 12, 2005
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
Let  be a completely positive map on  and let  be the associated GNS- -correspondence. We prove a result that implies, in particular, that the Cuntz-Pimsner algebra of  ,  , is strongly Morita equivalent to the Cuntz algebra  , where  is the index of  .
References:
-
- 1.
- D. Blecher, P. Muhly and V. Paulsen, Categories of operator modules (Morita equivalence and projective modules), Memoirs of the Amer. Math. Soc., Vol. 143, # 681, Providence, 2000. MR 1645699 (2000j:46132)
- 2.
- P. Muhly and B. Solel, Tensor Algebras over C*-Correspondences: Representations, Dilations, and C*-Envelopes, J. Functional Anal. 158 (1998), 389-457. MR 1648483 (99j:46066)
- 3.
- P. Muhly and B. Solel, On the Morita Equivalence of Tensor Algebras, Proc. London Math. Soc. 81 (2000), 113-168.MR 1757049 (2001g:46128)
- 4.
- P. Muhly and B. Solel, The Curvature and index of completely positive maps, Proc. London Math. Soc. 87 (2003), 748-778.MR 2005882 (2004i:47013)
- 5.
- G. Popescu, Von Neumann inequality for
 , Math. Scand. 68 (1991), 292-304. MR 1129595 (92k:47073)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
46L07, 46L08, 46M18, 47L30
Retrieve articles in all Journals with MSC
(2000):
46L07, 46L08, 46M18, 47L30
Additional Information:
Alberto
E.
Marrero
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Address at time of publication:
Department of Mathematics and Computer Science, Valparaiso University, Valparaiso, Indiana 46383-6493
Email:
amarrero@math.uiowa.edu
Paul
S.
Muhly
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email:
pmuhly@math.uiowa.edu
DOI:
10.1090/S0002-9939-05-08110-4
PII:
S 0002-9939(05)08110-4
Keywords:
Cuntz-Pimsner algebras,
completely positive maps,
Morita equivalence
Received by editor(s):
November 2, 2004
Posted:
August 12, 2005
Additional Notes:
The research of the authors was supported in part by a grant from the National Science Foundation, DMS-0070405. The first author was also supported by a GAANN Fellowship and the Sloan Foundation.
Communicated by:
David R. Larson
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org