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The numerical range of an unbounded operator


Author: M. J. Crabb
Journal: Proc. Amer. Math. Soc. 55 (1976), 95-96
DOI: https://doi.org/10.1090/S0002-9939-1976-0394244-1
MathSciNet review: 0394244
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Abstract | References | Additional Information

Abstract: The numerical range of an unbounded linear operator on a complex Banach space is the whole complex plane.


References [Enhancements On Off] (What's this?)

  • [1] M. J. Crabb and A. M. Sinclair, On the boundary of the spatial numerical range, Bull. London Math. Soc. 4 (1972), 17–19. MR 0308815, https://doi.org/10.1112/blms/4.1.17
  • [2] J. R. Giles and G. Joseph, The numerical ranges of unbounded operators, Bull. Austral. Math. Soc. 11 (1974), 31–36. MR 0370220, https://doi.org/10.1017/S0004972700043598
  • [3] E. Hille, Generalizations of Landau's inequality to linear operators, Conf. on Linear Operators and Approximation, Oberwolfach, August 1971.
  • [4] A. N. Kolmogorov, On inequalities between the upper bounds of the successive derivatives of an arbitrary function on an infinite interval, Učen. Zap. Moskov. Gos. Univ. Matematika 30 (1939), 3-13; English transl., Amer. Math. Soc. Transl. (1) 2 (1962), 233-243. MR 1, 298.


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0394244-1
Keywords: Numerical range, unbounded linear operator
Article copyright: © Copyright 1976 American Mathematical Society