Positive Linear Maps of Operator Algebras
This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum
- PDF / 1,445,023 Bytes
- 135 Pages / 439.37 x 666.142 pts Page_size
- 84 Downloads / 228 Views
For further volumes: www.springer.com/series/3733
Erling Størmer
Positive Linear Maps of Operator Algebras
Erling Størmer Department of Mathematics University of Oslo Oslo, Norway
ISSN 1439-7382 Springer Monographs in Mathematics ISBN 978-3-642-34368-1 ISBN 978-3-642-34369-8 (eBook) DOI 10.1007/978-3-642-34369-8 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2012954674 Mathematics Subject Classification (2010): 46L60, 46L70 © Springer-Verlag Berlin Heidelberg 2013 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Introduction
The study of positive maps of C ∗ -algebras started around 1950 with Kadison’s generalized Schwarz inequality and characterizations of isometries of C ∗ -algebras, [35, 36]. A few years later Stinespring introduced completely positive maps and showed his famous dilation theorem [70]. A little later Tomiyama proved some of the basic results on positive projections of von Neumann algebras onto von Neumann subalgebras, called conditional expectations [92]. After that the theory gradually developed, but with rather few people involved. A change came in the 1990’s when it became clear that positive maps are important in the study of entanglement in quantum information theory. Since then the interest in the s
Data Loading...
