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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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A remark on expanding maps
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by Kung Ching Chang and Shu Jie Li PDF
Proc. Amer. Math. Soc. 85 (1982), 583-586 Request permission

Abstract:

In this paper we discuss the following problem stated by L. Nirenberg: Let $T$ be an expanding map $H \to H$ ($H$ is a Hilbert space) with $T(0) = 0$. Suppose $T$ maps a neighborhood of the origin onto a neighborhood of the origin. Does $T$ map $H$ onto $H$? We answer positively the problem when $T$ is differentiable.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 583-586
  • MSC: Primary 47H15; Secondary 58C15
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0660608-4
  • MathSciNet review: 660608