Hostname: page-component-84b7d79bbc-c654p Total loading time: 0 Render date: 2024-07-26T04:51:48.651Z Has data issue: false hasContentIssue false
  • English
  • Français

C*-ideals generated by polynomials

Published online by Cambridge University Press:  20 January 2009

Paul Tapper
Paul Tapper
Affiliation:
Department of pure Mathematics, Leeds University, Leeds, LS2 9JT, United Kingdom E-mail address: paul_tapper@hotmail.com
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The *-algebra A1 is defined to be the free unital *-algebra with one generator x. A *-ideal I of A1 is defined to be a C*-ideal if A1/I may be embedded into a C*-algebra. It is proved that if I is a *-ideal of A1 generated by polynomials in A1, then I is a C*-ideal. This is not true for general *-ideals of A1.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 2 , June 1999 , pp. 305 - 309
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

REFERENCES

1.Coburn, L. A., The C*-algebra generated by an isometry, Bull. Amer. Math. Soc. 73 (1967), 722–726.Google Scholar
2.Goodearl, K. R. and Menal, P., Free and residually finite-dimensional C*-algebras, J. Funct. Anal. 90 (1990), 391–410.Google Scholar
3.Tapper, P. N., Embedding *-algebras into C*-algebras and C*-ideals generated by words, J. Operator Theory, submitted.Google Scholar