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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A remark on expanding maps

Authors: Kung Ching Chang and Shu Jie Li
Journal: Proc. Amer. Math. Soc. 85 (1982), 583-586
MSC: Primary 47H15; Secondary 58C15
MathSciNet review: 660608
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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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PII: S 0002-9939(1982)0660608-4
Keywords: Expanding map, Hadamard implicit function theorem, potential operator
Article copyright: © Copyright 1982 American Mathematical Society