Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-12-04T22:13:18.282Z Has data issue: false hasContentIssue false
  • English
  • Français

Spectral radius formulae

Published online by Cambridge University Press:  20 January 2009

G. J. Murphy  and
T. T. West
G. J. Murphy
Affiliation:
School of Mathematics, Trinity College, Dublin
T. T. West
Affiliation:
School of Mathematics, Trinity College, Dublin
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.

If A is a complex Banach algebra (not necessarily unital) and x∈A, σ(x) will denote the spectrum and spectral radius of x in A. If I is a closed two-sided ideal in A let x + I denote the coset in the quotient algebra A/I containing x. Then

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 3 , October 1979 , pp. 271 - 275
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

(1) Barnes, B. A., Examples of modular annihilator algebras, Rocky Mountain J. Math. 1 (1971), 657–663.CrossRefGoogle Scholar
(2) Dixmier, J., Les C*-algebres et leurs representations (Gauthier-Villars, Paris, 1964).Google Scholar
(3) Pedersen, G. K., Spectral formulas in quotient C*-algebras, Math. Zeit. 148 (1976), 299–300.CrossRefGoogle Scholar
(4) Rota, G. C., On models for linear operators, Comm. Pure Appl. Math. 13 (1960), 469–472.CrossRefGoogle Scholar
(5) Smyth, M. R. F., Riesz theory in Banach algebras, Math. Zeit. 145 (1975), 145–155.CrossRefGoogle Scholar
(6) Smyth, M. R. F., Riesz algebras, Proc. Roy. Irish Acad. 76(A) (1975), 327–333.Google Scholar
(7) Smyth, M. R. F., and West, T. T., The spectral radius formula in quotient algebras, Math. Zeit. 145 (1975), 157–161.CrossRefGoogle Scholar
(8) Stout, E. L., The theory of uniform algebras (Bogden and Quigley, Tarrytown-on-Hudson, 1971).Google Scholar