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PAUL A. FUHRMANN
Department of Mathematics
Ben Gurion University of the Negev
Beer Sheva, Israel
Linear Systems
and Operators in
Hilbert Space
British Library Cataloguing is Publication Data
Fuhrmann, Paul A.
Linear systems and operators in Hilbert space.
space operators
I. Title
515'.73 78 40976
ISBN 0-07-022589-3
LINEAR SYSTEMS AND OPERATORS
IN HILBERT SPACE
Copyright ® 1981 by McGraw-Hill, Inc. All rights reserved.
No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any
means, electronical, mechanical, photocopying, recording or otherwise,
without the prior written permission of the publisher.
2345 MOC 8321
CONTENTS
Chapter I. Linear algebra and finite dimensional systems
Introduction
and modules 2
modules 6
3. The Smith canonical form 12
of linear transformations 15
systems 28
, observability, and realizations 31
7. Hankel matrices 32
and isomorphism 34
functions and their factorizations 38
theory 39
11. Polynomial system matrices 43
resultant theorem 46
13. Feedback 50
Notes and references 62
Chapter II. Operators in Hilbert space 63
I .Geometry of Hilbert space 63
2. Bounded operators in Hilbert space 70
3. Unbounded operators 77
theorems 83
5. The spectral theorem 93
representations 104
7. The Douglas factorization theorem and related results 124
, isometries, and the Wold position 126
, dilations, and models 129
vii
viii CONTENTS
10. Semigroups of operators
11. The lifting theorem
12. Elemen