A missing theorem on dual spaces
Functional Analysis
2024-05-13 v3 Classical Analysis and ODEs
Operator Algebras
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.
Cite
@article{arxiv.2405.01133,
title = {A missing theorem on dual spaces},
author = {David P. Blecher},
journal= {arXiv preprint arXiv:2405.01133},
year = {2024}
}
Comments
Error in early lemma (Proposition 2.3) endangers Theorem 4.1. Result is valid assuming the conclusions of Proposition 2.3 for the map q in Theorem 4.1