American Mathematical Soc., 1973 - 108 Seiten
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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The structure of
Critical points and group algebras
Idempotents and logarithms
Boundaries and Gleason parts
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abelian absolutely continuous analytic Banach space Bohr compactification bounded C*-algebra Čech cohomology Chapter closed ideal cohomology sequence cokernel commutative measure algebra complex homomorphism concentrated conclude containing the identity convolution measure algebra COROLLARY critical point defined denote dense dual group element h equation fact fe f finite follows functors Furthermore Gelfand transform group G Haar measure Hausdorff space Hence homotopy HP(S idempotent implies induced infinite product injective invertible isomorphic kernel L-homomorphism L-ideal L-space L-subalgebra L-subspace l.c. a group LEMMA linear span locally compact logarithm LP(R maximal group algebra measure algebra minimal element neighborhood nondiscrete nonzero norm Note operator pair PROPOSITION prove Rad L(G restriction map Rudin satisfies semicharacter semisimple semisimple measure algebra Shilov boundary spectrum strong boundary strong topology structure semigroup subgroup subsemigroup subset surjective theorem topological semigroup u e M(G u o a unique vanish weak zero