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On numerical ranges of operators on locally convex spaces

Published online by Cambridge University Press:  09 April 2009

J. R. Giles ,
G. Joseph ,
D. O. Koehler  and
B. Sims
J. R. Giles
Affiliation:
The University of Newcastle, N.S.W., Australia
G. Joseph
Affiliation:
Miami University, Oxford, Ohio, U.S.A.
D. O. Koehler
Affiliation:
The University of New England, N.S.W., Australia
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Numerical range theory for linear operators on normed linear spaces and for elements of normed algebras is now firmly established and the main results of this study are conveniently presented by Bonsall and Duncan in (1971) and (1973). An extension of the spatial numerical range for a class of operators on locally convex spaces was outlined by Moore in (1969) and (1969a), and an extension of the algebra numerical range for elements of locally m-convex algebras was presented by Giles and Koehler (1973). It is our aim in this paper to contribute further to Moore's work by extending the concept of spatial numerical range to a wider class of operators on locally convex spaces.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 4 , November 1975 , pp. 468 - 482
Copyright
Copyright © Australian Mathematical Society 1975

References

Bonsall, F. F. and Duncan, J. (1971), Numerical range of operators on normed spaces and of elements of normed algebras, (Lond. Math. Soc. Lecture Note Series 2, Cambridge 1971).Google Scholar
Bonsall, F. F. and Duncan, J. (1973), ‘Numerical ranges II’ (Lond. Math. Soc. Lecture Note Series 10, Cambridge 1973).Google Scholar
Giles, J. R. and Koehler, D. O. (1973), ‘On numerical ranges of elements of locally m-convex algebras’, Pacific J. Math. 49, 79–91.CrossRefGoogle Scholar
Holmes, R. B. (1968), ‘A formula for the spectral radius of an operator’, Amer. Math. Monthly 75, 163–166.Google Scholar
Michael, E. A. (1952), ‘Locally multiplicatively convex topological algebras’, Mem. Amer. Math. Soc. 11 (1952).Google Scholar
Moore, R. T. (1969), ‘Banach algebras of operators on locally convex spaces’, Bull. Amer. Math. Soc. 75, 68–73.Google Scholar
Moore, R. T. (1969 a), ‘Adjoints, numerical ranges, and spectra of operators on locally convex spaces’, Bull. Amer. Math. Soc. 75, 85–90.CrossRefGoogle Scholar