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).
| Original language | English |
|---|---|
| Pages (from-to) | 145-150 |
| Number of pages | 6 |
| Journal | Journal of Functional Analysis |
| Volume | 59 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 15 Oct 1984 |
| Externally published | Yes |
Bibliographical note
Acknowledgment:We thank H. Brezis for introducing us to this problem.
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