Octahedrality and Gâteaux smoothness

[EN] We prove that every Banach space admitting a Gâteaux smooth norm and containing a complemented copy of I1 has an equivalent renorming which is simultaneously Gâteaux smooth and octahedral. This is a partial solution to an open problem from the early nineties. (c) 2024 The Author(s). Published b...

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Bibliographic Details
Authors: Cobollo-Gómez, Christian|||0000-0002-5901-5798, Hájek, P.
Format: article
Publication Date:2025
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/211985
Online Access:https://riunet.upv.es/handle/10251/211985
Access Level:Open access
Keyword:Renorming
Octahedral
Gâteaux
Geometry of Banach spaces
Description
Summary:[EN] We prove that every Banach space admitting a Gâteaux smooth norm and containing a complemented copy of I1 has an equivalent renorming which is simultaneously Gâteaux smooth and octahedral. This is a partial solution to an open problem from the early nineties. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC license (http://creativecommons .org /licenses /by -nc /4 .0/).