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arXiv · 2405.01133

A missing theorem on dual spaces

David P. Blecher
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Abstract

We answer in the affirmative the surprisingly difficult questions: If a complex Banach space possesses a real predual X, then is X a complex Banach space? If a complex Banach space possesses a real predual, then does it have a complex predual? We also answer the analogous questions for operator spaces, that is spaces of operators on a Hilbert space, up to complete isometry. Indeed we use operator space methods to solve the Banach space question above.

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David P. Blecher. 2024-05-02. A missing theorem on dual spaces. https://arxiv.org/abs/2405.01133

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