On a problem of Nirenberg concerning expanding maps

Jean-Michel Morel; Heinrich Steinlein

doi:10.1016/0022-1236(84)90057-0

On a problem of Nirenberg concerning expanding maps

Jean-Michel Morel
, Heinrich Steinlein

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

13 Citations (Scopus)

Abstract

Let X be a Banach space and T:X → X a continuous map, which is expanding (i.e., ∥Tu - Tv∥ ≥ ∥u - v∥ for all u, v ε{lunate} X) and such that T(X) has a nonempty interior. Does this guarantee that T is onto? We give a counterexample in the case of X=L¹(N). © 1984.

Original language	English
Pages (from-to)	145-150
Journal	Journal of Functional Analysis
Volume	59
Issue number	1
DOIs	https://doi.org/10.1016/0022-1236(84)90057-0
Publication status	Published - 15 Oct 1984
Externally published	Yes

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Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

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AU - Steinlein, Heinrich

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N2 - Let X be a Banach space and T:X → X a continuous map, which is expanding (i.e., ∥Tu - Tv∥ ≥ ∥u - v∥ for all u, v ε{lunate} X) and such that T(X) has a nonempty interior. Does this guarantee that T is onto? We give a counterexample in the case of X=L1(N). © 1984.

AB - Let X be a Banach space and T:X → X a continuous map, which is expanding (i.e., ∥Tu - Tv∥ ≥ ∥u - v∥ for all u, v ε{lunate} X) and such that T(X) has a nonempty interior. Does this guarantee that T is onto? We give a counterexample in the case of X=L1(N). © 1984.

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DO - 10.1016/0022-1236(84)90057-0

M3 - RGC 21 - Publication in refereed journal

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SP - 145

EP - 150

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

ER -

On a problem of Nirenberg concerning expanding maps

Abstract

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