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Let $E,F$ be real Banach spaces where $E$ is reflexive. Let $i:E \to F$ be a surjective isometry. If $i$ is linear, then $F$ is also reflexive.

Could you give an example where $F$ is not reflexive?

Thank you so much for your elaboration!

Akira
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1 Answers1

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Due to Mazur-Ulam theorem, there is no such example.

Anne Bauval
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