Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The numerical range and the essential numerical range

Author: J. P. Williams
Journal: Proc. Amer. Math. Soc. 66 (1977), 185-186
MSC: Primary 47A10
MathSciNet review: 0458203
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A10

Retrieve articles in all journals with MSC: 47A10

Additional Information

Keywords: Operator on Hilbert space, numerical range, essential numerical range
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society