SpringerBriefs in MathematicsThis 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 Since 1997 the research devoted to these mathematical objects has grown greatly. A simple search in the database MathSciNet of the American Mathematical Society with the keyword "numerical range" in the title reveals more than 300 papers published after 1997 while the same search with the keyword "numerical radius" adds other 100, showing an immense interest on the subject by numerous researchers working in different fields of modern mathematics. If no restrictions for the year are imposed, the number of papers with those keywords in the title exceeds 1,000. However, the size of the areas of applications for numerical ranges and radii is very difficult to estimate. If we perform a search looking for the publications where in a way or another the concept of "numerical range" is used, we can get more than 1,550 items.The present monograph is focused on numerical radius inequalities for bounded linear operators on complex Hilbert spaces for the case of one and two operators.The book is intended for use both by researchers in various fields of linear operator theory in Hilbert spaces and mathematical inequalities, domains which have grown exponentially in the last decade, and by postgraduate students and scientists applying inequalities in their specific areas.I...
