Hostname: page-component-84b7d79bbc-c654p Total loading time: 0 Render date: 2024-07-25T16:21:29.230Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear and convex combinations of projections in simple C* -algebras

Published online by Cambridge University Press:  14 November 2011

A. Guyan Robertson
A. Guyan Robertson
Affiliation:
Department of Mathematics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, Scotland
Get access Rights & Permissions [Opens in a new window]

Synopsis

Motivated by results of G. K. Pedersen, showing how a simple C*-algebra must contain an abundance of projections whenever it contains a single nontrivial projection, we provide generalisations and new proofs using more algebraic methods.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 101 , Issue 1-2 , 1985 , pp. 125 - 129
Copyright
Copyright © Royal Society of Edinburgh 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Blackadar, B. E.. A simple unital projectionless C*-algebra. J. Operator Theory 5 (1981), 63–71.Google Scholar
2Connes, A.. An analogue of the Thorn isomorphism for crossed products of a C*-algebra by an action of ℝ. Adv. in Math. 39 (1981), 35–55.CrossRefGoogle Scholar
3Cuntz, J.. The structure of multiplication and addition in simple C*-algebras. Math. Scand. 40 (1977), 215–233.CrossRefGoogle Scholar
4Dixmier, J.. Les algèbres d'opérateurs dans les espaces Hilbertiens (Paris: Gauthier-Villars, 1969).Google Scholar
5Dixmier, J.. Les C*-algèbres et leurs représentations (Paris: Gauthier-Villars, 1964).Google Scholar
6Fack, T.. Finite sums of commutators in C*-algebras. Ann. Inst. Fourier, Grenoble 32 (1982), 129–137.Google Scholar
7Goodearl, K.. Notes on real and complex C*-algebras (Norwich: Shiva, 1982).Google Scholar
8Herstein, I. N.. Lie and Jordan structures in simple associative rings. Bull. Amer. Math. Soc. 67 (1961), 517–531.CrossRefGoogle Scholar
9Pedersen, G. K.. The linear span of projections in simple C*-algebras. J. Operator Theory 4 (1980), 289–296.Google Scholar
10Rieffel, M. A.. Dimension and stable rank in the K-theory of C*-algebras. Proc. London Math. Soc. 46 (1983), 301–333.CrossRefGoogle Scholar