Lectures on Amenability

2002
ISBN: 978-3-540-42852-7
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1774, 302 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 482 g

Reihe: Lecture Notes in Mathematics

The notion of amenability has its origins in the beginnings of modern measure theory: Does a finitely additive set function exist which is invariant under a certain group action? Since the 1940s, amenability has become an important concept in abstract harmonic analysis (or rather, more generally, in the theory of semitopological semigroups). In 1972, B.E. Johnson showed that the amenability of a locally compact group G can be characterized in terms of the Hochschild cohomology of its group algebra L^1(G): this initiated the theory of amenable Banach algebras. Since then, amenability has penetrated other branches of mathematics, such as von Neumann algebras, operator spaces, and even differential geometry. Lectures onAmenability introduces second year graduate students to this fascinating area of modern mathematics and leads them to a level from where they can go on to read original papers on the subject. Numerous exercises are interspersed in the text.

Zielgruppe

Research

Autoren/Hrsg.

Runde, Volker

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

Paradoxical decompositions.- Amenable, locally comact groups.- Amenable Banach algebras.- Exemples of amenable Banach algebras.- Amenability-like properties.- Banach homology.- C* and W*-algebras.- Operator amenability.- Geometry of spaces of homomorphisms.- Open problems: Abstract harmonic analysis.- Tensor products.- Banach space properties.- Operator spaces.- List of symbols.- References.- Index.