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Constants relating a Hermitian operator and its square

Published online by Cambridge University Press:  24 October 2008

J. R. Partington
J. R. Partington
Affiliation:
Trinity College, Cambridge
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Extract

Let T be a linear operator on a complex normed space X. Its spatial numerical range V(T) is denned as

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 2 , March 1979 , pp. 325 - 333
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

(1)Bauer, F. L., Stoer, J. and Witzgall, C.Absolute and monotonic norms. Numer. Math. 3 (1961), 257–264.CrossRefGoogle Scholar
(2)Bollobás, B.A characterization of the circle and its application to hermitian operators. Proc. Cambridge Philos. Soc. 74 (1973), 69–72.CrossRefGoogle Scholar
(3)Bollobás, B.The spatial numerical range and powers of an operator. J. London Math. Soc. 7 (1973), 435–440.Google Scholar
(4)BollobáS, B. and Eldridge, S. E.The numerical range of unbounded linear operators. Bull. Austral. Math. Soc. 12 (1975), 23–25.CrossRefGoogle Scholar
(5)BollobáS, B. and Galanis, E.An inequality involving a hermitian operator and its square in a normed space. Bull. Soc. Math. Grèce 17 (1976), 44–49.Google Scholar
(6)Bonsall, F. F. and Duncan, J. Numerical ranges of operators on normed spaces and elements of normed algebras. London Math. Soc. Lecture Notes 2 (Cambridge University Press, 1971).Google Scholar
(7)Bonsall, F. F. and Duncan, J. Numerical ranges II. London Math. Soc. Lecture Notes 10 (Cambridge University Press, 1973).Google Scholar
(8)Crabb, M. J.The numerical range of an unbounded operator. Proc. Amer. Math. Soc. 55 (1976), 95–96.CrossRefGoogle Scholar
(9)Giles, J. R. and Joseph, G.The numerical range of unbounded operators. Bull. Austral. Math. Soc. 11 (1974), 31–36.CrossRefGoogle Scholar
(10)Kolmogorov, A. N.On inequalities between the upper bounds of the successive derivatives of an arbitrary function on an infinite interval. Amer. Math. Soc. Translations (1) 2 (1962), 233–243.Google Scholar
(11)Partington, J. R. Hermitian operators for absolute norms and absolute direct sums. To appear in Linear Algebra and its Applications.Google Scholar
(12)Schneider, H. and Turner, R. E. L.Matrices hermitian for an absolute norm. Linear and Multilinear Algebra 1 (1973), 9–31.CrossRefGoogle Scholar
(13)Sinclair, A. M.The norm of a Hermitian element in a Banach algebra. Proc. Amer. Math. Soc. 28 (1971), 446–450.CrossRefGoogle Scholar
(14)Tam, K. W.Isometries of certain function spaces. Pacific J. Math. 31 (1969), 233–246.CrossRefGoogle Scholar
(15)Zygmund, A.Trigonometric Series I (Cambridge University Press, 1959).Google Scholar