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The local resolvent set of a locally Lipschitzian transformation is open

Author: E. Lee May
Journal: Proc. Amer. Math. Soc. 55 (1976), 329-333
MSC: Primary 47H99
MathSciNet review: 0410500
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Abstract: The purpose of this paper is to prove that if $ p$ is a point of a complex Banach space $ H$ at which the nonlinear transformation $ T$ on $ H$ is locally Lipschitzian, then the local resolvent set of $ T$ at $ p$ is open.

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

  • [1] E. R. Lorch, Spectral theory, University Texts in the Mathematical Sciences, Oxford Univ. Press, New York, 1962. MR 25 #427. MR 0136967 (25:427)
  • [2] E. L. May, Jr., Localizing the spectrum, Pacific J. Math. 44 (1973), 211-218. MR 47 #4089. MR 0315540 (47:4089)

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Keywords: Local resolvent set, nonlinear transformation, locally Lipschitzian, successive approximation, Banach space
Article copyright: © Copyright 1976 American Mathematical Society

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