A missing theorem on dual spaces

2024/05/02 by David P. Blecher, Blecher, David P.
Mathematics · #Advanced Banach Space Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2405.01133

openalex publication_date 2024/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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