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 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
DOI: https://doi.org/10.1090/S0002-9939-1976-0410500-2
MathSciNet review: 0410500
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H99

Retrieve articles in all journals with MSC: 47H99


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0410500-2
Keywords: Local resolvent set, nonlinear transformation, locally Lipschitzian, successive approximation, Banach space
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society