Elements of Hilbert Spaces and Operator Theory
The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory an
- PDF / 5,576,853 Bytes
- 528 Pages / 453.543 x 683.15 pts Page_size
- 38 Downloads / 343 Views
Elements of Hilbert Spaces and Operator Theory
Elements of Hilbert Spaces and Operator Theory
Harkrishan Lal Vasudeva
Elements of Hilbert Spaces and Operator Theory With contributions from Satish Shirali
123
Harkrishan Lal Vasudeva Indian Institute of Science Education and Research Mohali, Punjab India
ISBN 978-981-10-3019-2 DOI 10.1007/978-981-10-3020-8
ISBN 978-981-10-3020-8
(eBook)
Library of Congress Control Number: 2016957499 © Springer Nature Singapore Pte Ltd. 2017 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 Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
To Siddhant, Ashira and Shrayus
Preface
Algebraic and topological structures compatibly placed on the same underlying set lead to the notions of topological semigroups, groups and vector spaces, among others. It is then natural to consider concepts such as continuous homomorphisms and continuous linear transformations between above-said objects. By an ‘operator’, we mean a continuous linear transformation of a normed linear space into itself. Functional analysis was developed around the turn of the last century by the pioneering work of Banach, Hilbert, von Neumann, Riesz and others. Within a few years, after an amazing burst of activity, it was well developed as a major branch of mathematics. It is a unifying framework for many diverse areas such as Fourier series, differential and integral equations, analytic function theory and analytic number theory. The subject continues to grow and attracts the attention of some of the finest mathematicians of the era. A generalisation of the methods of vector algebra and calculus manifests itself in the mathematical concept of a Hilbert space, named after the celebrated mathematician Hilbert. It extends these methods from two-dimensional and three-dimensional Euclidean
Data Loading...
