Journal article
MORITA EQUIVALENCE OF OPERATOR ALGEBRAS AND THEIR C-ENVELOPES
The Bulletin of the London Mathematical Society, Vol.31(5), pp.581-591
09/1999
DOI: 10.1112/S0024609399005962
Abstract
If two operator algebras A and B are strongly Morita
equivalent (in the sense of [5]), then their C*-
envelopes C*(A) and C*(B) are
strongly Morita equivalent (in the usual C*-algebraic sense due to Rieffel).
Moreover, if Y is an equivalence bimodule for a (strong) Morita
equivalence of A and B, then the
operation, Y[otimes ]hA−, of tensoring with Y,
gives a bijection between the boundary representations of C*(A)
for A and the boundary representations of C*(B) for B.
Thus the ‘noncommutative Choquet boundaries’
of Morita equivalent A and B are the same. Other important
objects associated with an operator algebra
are also shown to be preserved by Morita equivalence, such as boundary ideals, the Shilov boundary ideal,
Arveson's property of admissability, and the lattice of C*-algebras generated by an operator algebra.
Details
- Title: Subtitle
- MORITA EQUIVALENCE OF OPERATOR ALGEBRAS AND THEIR C-ENVELOPES
- Creators
- DAVID P BLECHER - Department of Mathematics, University of Houston, Houston, TX 77204-3476, USAPAUL S MUHLY - Department of Mathematics, University of Iowa, Iowa City, IA 52242, USAQIYUAN NA - Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
- Resource Type
- Journal article
- Publication Details
- The Bulletin of the London Mathematical Society, Vol.31(5), pp.581-591
- Publisher
- Cambridge University Press
- DOI
- 10.1112/S0024609399005962
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- Number of pages
- 11
- Language
- English
- Date published
- 09/1999
- Academic Unit
- Mathematics; Statistics and Actuarial Science
- Record Identifier
- 9984083999402771
Metrics
5 Record Views