Separably Injective Banach Spaces
This monograph contains a detailed exposition of the up-to-date theory of separably injective spaces: new and old results are put into perspective with concrete examples (such as l∞/c0 and C(K) spaces, where K is a
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Antonio Avilés Félix Cabello Sánchez Jesús M. F. Castillo Manuel González Yolanda Moreno
Separably Injective Banach Spaces
Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis, Zurich Mario di Bernardo, Bristol Alessio Figalli, Austin Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gabor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, Paris and NY Catharina Stroppel, Bonn Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Antonio Avilés • Félix Cabello Sánchez • Jesús M.F. Castillo • Manuel González • Yolanda Moreno
Separably Injective Banach Spaces
123
Antonio Avilés Dpto. de Matemáticas Universidad de Murcia Murcia, Spain
Félix Cabello Sánchez Dpto. de Matemáticas Universidad de Extremadura Badajoz, Spain
Jesús M.F. Castillo Dpto. de Matemáticas Universidad de Extremadura Badajoz, Spain
Manuel González Dpto. de Matemáticas Universidad de Cantabria Santander, Spain
Yolanda Moreno Dpto. de Matemáticas Universidad de Extremadura Cáceres, Spain
ISSN 0075-8434 Lecture Notes in Mathematics ISBN 978-3-319-14740-6 DOI 10.1007/978-3-319-14741-3
ISSN 1617-9692 (electronic) ISBN 978-3-319-14741-3 (eBook)
Library of Congress Control Number: 2016935425 Mathematics Subject Classification (2010): 46A22, 46B03, 46B08, 46M10, 46M18, 46B26, 54B30 © 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
Preface
The Plot Injective Banach spaces are those spaces that allow the extension of any operator with values in them to any superspace. Finite dimensional and `1 are the simplest examples of injective spaces. When a Banach space is injective, there automatically appears a constant that controls the norms of the extensions. At the ot
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