Let be the standard coding for separable Banach spaces as subspaces of . In these notes, we show that if is a Borel subset of spaces with separable dual, then the assignment can be realized by a Borel function . Moreover, this assignment can be done in such a way that the functional evaluation is still well defined (Theorem 1). Also, we prove a Borel parametrized version of Zippin’s theorem, i.e., we prove that there exists and a Borel function that assigns for each an isomorphic copy of inside of (Theorem 5).
Soit le codage standard des espaces de Banach séparables comme sous-espaces de . Dans ce papier, on montre que si est un sous-ensemble borélien d’espaces à dual séparable, alors l’application peut être réalisée par une fonction borélienne de à . En outre, cette application peut être construite de manière que l’évaluation fonctionnelle est toujours bien définie (Théorème 1). Par ailleurs, on démontre une version borélienne du théorème de Zippin. Plus précisément, on démontre qu’il existe et une fonction borélienne qui à chaque associe une copie isomorphe à à l’intérieur de (Théorème 5).
Keywords: Banach spaces, duality, descriptive set theory, Zippin’s theorem
Mot clés : espaces de Banach, dualité, théorie descriptive des ensembles, théorème de Zippin.
Braga, Bruno de Mendonça 1
@article{AIF_2015__65_6_2413_0, author = {Braga, Bruno de Mendon\c{c}a}, title = {Duality on {Banach} spaces and a {Borel} parametrized version of {Zippin{\textquoteright}s} theorem}, journal = {Annales de l'Institut Fourier}, pages = {2413--2435}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {65}, number = {6}, year = {2015}, doi = {10.5802/aif.2991}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2991/} }
TY - JOUR AU - Braga, Bruno de Mendonça TI - Duality on Banach spaces and a Borel parametrized version of Zippin’s theorem JO - Annales de l'Institut Fourier PY - 2015 SP - 2413 EP - 2435 VL - 65 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2991/ DO - 10.5802/aif.2991 LA - en ID - AIF_2015__65_6_2413_0 ER -
%0 Journal Article %A Braga, Bruno de Mendonça %T Duality on Banach spaces and a Borel parametrized version of Zippin’s theorem %J Annales de l'Institut Fourier %D 2015 %P 2413-2435 %V 65 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2991/ %R 10.5802/aif.2991 %G en %F AIF_2015__65_6_2413_0
Braga, Bruno de Mendonça. Duality on Banach spaces and a Borel parametrized version of Zippin’s theorem. Annales de l'Institut Fourier, Volume 65 (2015) no. 6, pp. 2413-2435. doi : 10.5802/aif.2991. https://aif.centre-mersenne.org/articles/10.5802/aif.2991/
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