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Spatial numerical range of an operator

Published online by Cambridge University Press:  24 October 2008

K. Tillekeratne
K. Tillekeratne
Affiliation:
Churchill College, Cambridge and University of Ceylon, Peradeniya, Ceylon
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Extract

0. Introduction. Let X be a normed space and let T be an operator on X. Let S(X) denote its unit sphere, {x ∈ X: ∥x∥ = 1}, B(X) = {x ∈ X: ∥x∥ ≤ 1} its unit ball, X′ its dual and ℬ(X) the normed algebra of bounded linear operators on X. Let II be the subset of the Cartesian product X × X′ defined by

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 3 , November 1974 , pp. 515 - 520
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Bollobás, B. Extremal algebras and the theory of numerical ranges (to appear in Proc. London Math. Soc.).Google Scholar
(2)Bollobás, B.The power inequality on Banach spaces, Proc. Cambridge Philos. Soc. 69 (1971), 411–415.CrossRefGoogle Scholar
(3a)Bonsall, F. F. and Duncan, , J. Numerical Ranges I (Cambridge University Press, 1971).Google Scholar
(3b)Bonsall, F. F. and Duncan, , J. Numerical Ranges II (Cambridge University Press, 1973).CrossRefGoogle Scholar
(4)Crabb, M. J.Some results on the numerical range of an operator. J. London Math. Soc. (2), 2 (1970), 741–745.CrossRefGoogle Scholar
(5)Crabb, M. J.The power inequality on nonmed spaces. Proc. Edinburgh Math. Soc. 17 (1971), 237–240.CrossRefGoogle Scholar
(6)Crabe, M. J., Dc, J. and McGregor, C. M.Mapping theorems and numerical radius. Proc. London Math. Soc. (3) 25 (1972), 486–503.CrossRefGoogle Scholar
(7)Duncan, J., McGregor, C. M., Pryce, J. D. and White, A. J.The numerical index of a normed space. J. London Math. Soc. (2), 2 (1970), 481–488.CrossRefGoogle Scholar
(8)Glickfield, B. W.On an inequality of a Banach algebra geometry and semi-inner product theory. Illinois J. Math. 14 (1970), 76–81.Google Scholar