Topics in Operator Theory PDF
Preview Topics in Operator Theory
Chicago Lectures in Mathematics topics in operator theory Richard Beals The University of Chicago Press Chicago and London Topics in Operator Theory Chicago Lectures in Mathematics topics in operator theory Richard Beals The University of Chicago Press Chicago and London Chicago Lectures in Mathematics Series Irving Kaplansky, Editor The Theory of Sheaves, by Richard G. Swan (1964) Topics in Ring Theory, by I. N. Herstein (1969) Fields and Rings, by Irving Kaplansky (1969) Infinite Abelian Group Theory, by Phillip A. Griffith (1970) Topics in Operator Theory, by Richard Beals (1971) Lie Algebras and Locally Compact Groups, by Irving Kaplansky (1971) Several Complex Variables, by Raghavan Narasimhan (1971) International Standard Book Number: 0-226-03985-4 Library of Congress Catalog Card Number: 70-147095 The University of Chicago Press, Chicago 60637 The University of Chicago Press, Ltd., London © 1971 by The University of Chicago All rights reserved Published 1971 Printed in the United States of America To the memory of my father CONTENTS Preface................................................................................................................ 1. Bounded operators in Hilbert space....................................................... * 2. Functional calculus for bounded and unbounded self-adjoint operators...................................................................................... H 3. Spectral measures and unitary groups................................................... 25 4. Vector and operator-valued functions on the line........................... 37 5. Spectral representation of self-adjoint and unitary operators.............................................................................................. 46 6. Shift operators and applications...........................................•................. 56 7. Continuous shifts and applications....................................................... ^y 8. Positive measures and harmonic functions........................... yg 9. Dissipative operators.............................................................. g^ 10. Characteristic functions...................................................... ^ 11. Factorization and invariant subspaces........................................... ^^g Notes and Bibliography.............................................................. Notation......................................................................................................... Index................................................................................................................. 12? vii
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