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On the numerical radius of an element of a normed algebra

Published online by Cambridge University Press:  18 May 2009

GH. Mocanu
Affiliation:
Faculty of Mathematics, University of Bucharest
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Let A be a unital normed algebra over the complex field ℂ, A' the dual space of A, i.e., the Banach space of all continuous linear functionals on A, and let S be the set of all states on A, i.e.,

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1974

References

REFERENCES

1.Bohnenblust, H. F. and Karlin, S., Geometrical properties of the unit sphere of Banach algebras, Ann. of Math. 62 (1955), 217229.Google Scholar
2.Bonsall, F. F., The numerical range of an element of a normed algebra, Glasgow Math. J. 10 (1969), 6872.CrossRefGoogle Scholar
3.Bonsall, F. F. and Duncan, J., Numerical ranges of operators on normed spaces and of elements of normed algebras, London Math. Soc. Lecture Note Series 2 (Cambridge, 1971).Google Scholar
4.Crabb, M. J., Numerical range estimates for the norms of iterated operators, Glasgow Math. J. 11 (1970), 8587.Google Scholar
5.Mocanu, Gh., Sur quelques critères de commutativité pour une algèbre de Banach, Analele Univ. Bucuresti Matematicǎ-Mecanicǎ 2 (1971), 127129.Google Scholar
6.Page, C. Le, Sur quelques conditions entrainant la commutativité dans les algèbres de Banach, C.R. Acad. Sci. Paris 265 (1967), 235237.Google Scholar
7.Stampfli, J. G., An extreme point theorem for inverses in a Banach algebra with identity, Proc. Cambridge Philos. Soc. 63 (1967), 993994.CrossRefGoogle Scholar