Integrals and Operators

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction

   • Irving E. Segal, Ray A. Kunze

   Pages 1-17

3. Basic Integrals

   • Irving E. Segal, Ray A. Kunze

   Pages 18-42

4. Measurable Functions and Their Integrals

   • Irving E. Segal, Ray A. Kunze

   Pages 43-92

5. Convergence and Differentiation

   • Irving E. Segal, Ray A. Kunze

   Pages 93-122

6. Locally Compact and Euclidean Spaces

   • Irving E. Segal, Ray A. Kunze

   Pages 123-151

7. Function Spaces

   • Irving E. Segal, Ray A. Kunze

   Pages 152-174

8. Invariant Integrals

   • Irving E. Segal, Ray A. Kunze

   Pages 175-205

9. Algebraic Integration Theory

   • Irving E. Segal, Ray A. Kunze

   Pages 206-238

10. Spectral Analysis in Hilbert Space

    • Irving E. Segal, Ray A. Kunze

    Pages 239-257

11. Group Representations and Unbounded Operators

    • Irving E. Segal, Ray A. Kunze

    Pages 258-302

12. Semigroups and Perturbation Theory

    • Irving E. Segal, Ray A. Kunze

    Pages 303-323

13. Operator Rings and Spectral Multiplicity

    • Irving E. Segal, Ray A. Kunze

    Pages 324-339

14. C*-Algebras and Applications

    • Irving E. Segal, Ray A. Kunze

    Pages 340-350

15. The Trace as a Non-Commutative Integral

    • Irving E. Segal, Ray A. Kunze

    Pages 351-364

16. Back Matter

    Pages 365-374

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TO THE SECOND EDITION Since publication of the First Edition several excellent treatments of advanced topics in analysis have appeared. However, the concentration and penetration of these treatises naturally require much in the way of technical preliminaries and new terminology and notation. There consequently remains a need for an introduction to some of these topics which would mesh with the material of the First Edition. Such an introduction could serve to exemplify the material further, while using it to shorten and simplify its presentation. It seemed particularly important as well as practical to treat briefly but cogently some of the central parts of operator algebra and higher operator theory, as these are presently represented in book form only with a degree of specialization rather beyond the immediate needs or interests of many readers. Semigroup and perturbation theory provide connections with the theory of partial differential equations. C*-algebras are important in har­ monic analysis and the mathematical foundations of quantum mechanics. W*-algebras (or von Neumann rings) provide an approach to the theory of multiplicity of the spectrum and some simple but key elements of the gram­ mar of analysis, of use in group representation theory and elsewhere. The v vi Preface to the Second Edition theory of the trace for operators on Hilbert space is both important in itself and a natural extension of earlier integration-theoretic ideas.

• C*-algebra
• Hilbert space
• Integrals
• convergence
• differential equation
• functional analysis
• harmonic analysis
• integral
• integration
• maximum
• measure
• operator
• operator algebra
• operator theory
• partial differential equation

• Massachusetts Institute of Technology, Cambridge, USA

  Irving E. Segal

• University of California at Irvine, Irvine, USA

  Ray A. Kunze

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