Hostname: page-component-84b7d79bbc-x5cpj Total loading time: 0 Render date: 2024-07-31T04:30:25.587Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical ranges of derivations

Published online by Cambridge University Press:  20 January 2009

J. Kyle
J. Kyle
Affiliation:
University of Technology, Loughborough, Leicestershire, England
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.

In this paper we shall examine the relationship between the numerical range of aninner derivation, and that of its implementing element.

Much of this paper is taken from the author's doctoral thesis (5) written at theUniversity of Newcastle upon Tyne with the helpful guidance of Professor B. E.Johnson. The author also acknowledges the financial support of the Science ResearchCouncil during the period of this research.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 21 , Issue 1 , March 1978 , pp. 33 - 39
Copyright
Copyright © Edinburgh Mathematical Society 1978

References

REFERENCES

(1) Bonsall, F. F. and Duncan, J., Complete normed algebras (Springer-Verlag, 1973).CrossRefGoogle Scholar
(2) Bonsall, F. F. and Duncan, J., Numerical ranges of operators and of elements of normed algebras (Lond. Math. Soc. Lecture Note Series (2), Cambridge University Press, 1971).CrossRefGoogle Scholar
(3) Bonsall, F. F. and Duncan, J., Numerical ranges II (Lond. Math. Soc. Lecture Note Series (10), Cambridge University Press, 1973).CrossRefGoogle Scholar
(4) Johnson, B. E., Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972).Google Scholar
(5) Kyle, J., Norms, spectra and numerical ranges of derivations, Ph.D. thesis (University of Newcastle upon Tyne, 1976).Google Scholar
(6) Kyle, J., Spectra of derivations, Math. Proc. Cambridge Philos. Soc. 82 (1977), 49–57.CrossRefGoogle Scholar
(7) Lumer, G. and Rosemblum, M., Linear operator equations, Proc. Amer. Math. Soc. 10 (1959), 32–41.CrossRefGoogle Scholar
(8) Sinclair, A. M., Jordan homomorphisms and derivations on semi-simple Banach algebras, Proc. Amer. Math. Soc. 24 (1970), 209–214.Google Scholar