The numerical range and the essential numerical range
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- by J. P. Williams PDF
- Proc. Amer. Math. Soc. 66 (1977), 185-186 Request permission
Abstract:
A simple proof is given of Lancaster’s theorem that the convex hull of the numerical and essential numerical ranges of a Hilbert space operator is the closure of the numerical range.References
- F. F. Bonsall and J. Duncan, Numerical ranges. II, London Mathematical Society Lecture Note Series, No. 10, Cambridge University Press, New York-London, 1973. MR 0442682, DOI 10.1017/CBO9780511662515
- J. Dixmier, Les fonctionnelles linéaires sur l’ensemble des opérateurs bornés d’un espace de Hilbert, Ann. of Math. (2) 51 (1950), 387–408 (French). MR 33445, DOI 10.2307/1969331
- John S. Lancaster, The boundary of the numerical range, Proc. Amer. Math. Soc. 49 (1975), 393–398. MR 372644, DOI 10.1090/S0002-9939-1975-0372644-2
- J. G. Stampfli and J. P. Williams, Growth conditions and the numerical range in a Banach algebra, Tohoku Math. J. (2) 20 (1968), 417–424. MR 243352, DOI 10.2748/tmj/1178243070
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 66 (1977), 185-186
- MSC: Primary 47A10
- DOI: https://doi.org/10.1090/S0002-9939-1977-0458203-3
- MathSciNet review: 0458203