**CBMS Regional Conference Series in Mathematics**

Volume: 16;
1973;
108 pp;
Softcover

MSC: Primary 43;
Secondary 46

**Print ISBN: 978-0-8218-1666-0
Product Code: CBMS/16**

List Price: $26.00

Individual Price: $20.80

**Electronic ISBN: 978-1-4704-2377-3
Product Code: CBMS/16.E**

List Price: $24.00

Individual Price: $19.20

# Measure Algebras

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*J. L. Taylor*

A co-publication of the AMS and CBMS

These notes were prepared in conjection with the NSF Regional Conference on measure algebras held at the University of Montana during the week of June 19, 1972. The original objective in preparing these notes was to give a coherent detailed, and simplified presentation of a body of material on measure algebras developed in a recent series of papers by the author. This material has two main thrusts: the first concerns an abstract characterization of Banach algebras which arise as algebras of measures under convolution (convolution measure algebras) and a semigroup representation of the spectrum (maximal ideal space) of such an algebra; the second deals with a characterization of the cohomology of the spectrum of a measure algebra and applications of this characterization to the study of idempotents, logarithms, and invertible elements. As the project progressed the original concept broadened. The final product is a more general treatment of measure algebras, although it is still heavily slanted in the direction of the author's own work.

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#### Reviews & Endorsements

This work is indeed impressive and extremely well-written. The author's work is a milestone in harmonic analysis, and this monograph is a clear, concise, and very readable account of one of the fundamental building blocks of the theory.

-- K. H. Hofman and Michael MisloveMathematical Reviews

#### Table of Contents

# Table of Contents

## Measure Algebras

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Preface v6 free
- Contents vii8 free
- Chapter 1: Orientation 110 free
- Chapter 2: L-spaces 1423
- Chapter 3: Convolution measure algebras 2332
- Chapter 4: Special examples 3342
- Chapter 5: The structure of S 4251
- Chapter 6: Cohomology of S 4857
- Chapter 7: Critical points and group algebras 5766
- Chapter 8: Idempotents and logarithms 7685
- Chapter 9: Invertible measures 8493
- Chapter 10: Boundaries and Gleason parts 9099
- References 103112
- Back Cover Back Cover1119