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Proceedings of the American Mathematical Society

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The numerical range and the essential numerical range


Author: J. P. Williams
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
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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 [Enhancements On Off] (What's this?)

  • [1] F. F. Bonsall and J. Duncan, Numerical ranges. II, London Math. Soc. Lecture Notes, Cambridge Univ. Press, Cambridge, 1973. MR 0442682 (56:1063)
  • [2] J. Dixmier, Les fonctionelles linéaires sur l'ensemble des opérateurs bornés d'un espace de Hilbert, Ann. of Math. (2) 51 (1950), 387-408. MR 11, 441. MR 0033445 (11:441e)
  • [3] John Lancaster, The boundary of the numerical range, Proc. Amer. Math. Soc. 49 (1975), 393-398. MR 51 #8851. MR 0372644 (51:8851)
  • [4] J. G. Stampfli and J. P. Williams, Growth conditions and the numerical range in a Banach algebra, Tôhoku Math. J. (2) 20 (1968), 417-424. MR 39 #4674. MR 0243352 (39:4674)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0458203-3
Keywords: Operator on Hilbert space, numerical range, essential numerical range
Article copyright: © Copyright 1977 American Mathematical Society

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