Open Problems in the Geometry and Analysis of Banach Spaces
This is a collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts
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Problems in the Geometry and Analysis of Banach Spaces
Open Problems in the Geometry and Analysis of Banach Spaces
Antonio J. Guirao • Vicente Montesinos Václav Zizler
Open Problems in the Geometry and Analysis of Banach Spaces
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Antonio J. Guirao Departamento de Matemática Aplicada Instituto de Matemática Pura y Aplicada Universitat Politècnica de València Valencia, Spain
Vicente Montesinos Departamento de Matemática Aplicada Instituto de Matemática Pura y Aplicada Universitat Politècnica de València Valencia, Spain
Václav Zizler Department of Mathematical and Statistical Sciences University of Alberta Alberta, Canada
ISBN 978-3-319-33571-1 DOI 10.1007/978-3-319-33572-8
ISBN 978-3-319-33572-8 (eBook)
Library of Congress Control Number: 2016939618 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Dedicated to the memory of Joram Lindenstrauss, Aleksander Pełczy´nski, and Manuel Valdivia
Preface
This is a commented collection of some easily formulated open problems in the geometry and analysis on Banach spaces, focusing on basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology, and nonlinear geometry. The collection consists of some commented questions that, to our best knowledge, are open. In some cases, we associate the problem with the person we first learned it from. We apologize if it may turn out that this person was not the original source. If we took the problem from a recent book, instead of referring to the author of the problem, we sometimes refer to that bibliographic source. We apologize that some problems might have already been solved. Some of the problems are longstanding open problems, some are recent, some are m
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