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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Pathwise connectivity of the spatial numerical range
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by Tofik Y. Kuliyev PDF
Proc. Amer. Math. Soc. 122 (1994), 1173-1174 Request permission

Abstract:

In this paper we prove that the spatial numerical range of a given operator on a separable Banach space is pathwise connected.
References
  • George Luna, On the numerical range in reflexive Banach spaces, Math. Ann. 231 (1977/78), no. 1, 33–38. MR 500208, DOI 10.1007/BF01360026
  • F. F. Bonsall and J. Duncan, Numerical ranges of operators on normed spaces and of elements of normed algebras, London Mathematical Society Lecture Note Series, vol. 2, Cambridge University Press, London-New York, 1971. MR 0288583
  • Herbert Weigel, Reflexivity and numerical range, Exposition. Math. 3 (1985), no. 4, 373–374. MR 844417
  • Ryszard Engelking, General topology, 2nd ed., Sigma Series in Pure Mathematics, vol. 6, Heldermann Verlag, Berlin, 1989. Translated from the Polish by the author. MR 1039321
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 122 (1994), 1173-1174
  • MSC: Primary 47A12
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1211582-1
  • MathSciNet review: 1211582