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.

Readership

Reviews

"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

• Orientation
• \(L\)-spaces
• Convolution measure algebras
• Special examples
• The structure of \(\hat S\)
• Cohomology of \(\hat S\)
• Critical points and group algebras
• Idempotents and logarithms
• Invertible measures
• Boundaries and Gleason parts
• References