Buch, Englisch, Band 40, 192 Seiten, Gewicht: 369 g
Reihe: University Lecture Series
Buch, Englisch, Band 40, 192 Seiten, Gewicht: 369 g
Reihe: University Lecture Series
ISBN: 978-0-8218-4137-2
Verlag: American Mathematical Society
The ``infinite-dimensional groups' in the title refer to unitary groups of Hilbert spaces, the infinite symmetric group, groups of homeomorphisms of manifolds, groups of transformations of measure spaces, etc. The book presents an approach to the study of such groups based on ideas from geometric functional analysis and from exploring the interplay between dynamical properties of those groups, combinatorial Ramsey-type theorems, and the phenomenon of concentration of measure. The
dynamics of infinite-dimensional groups is very much unlike that of locally compact groups. For instance, every locally compact group acts freely on a suitable compact space (Veech). By contrast, a 1983 result by Gromov and Milman states that whenever the unitary group of a separable Hilbert space continuously acts on a compact space, it has a common fixed point. In the book, this new fast-growing theory is built strictly from well-understood examples up. The book has no close counterpart and is based on recent research articles. At the same time, it is organized so as to be reasonably self-contained. The topic is essentially interdisciplinary and will be of interest to mathematicians working in geometric functional analysis, topological and ergodic dynamics, Ramsey theory, logic and descriptive set theory, representation theory, topological groups, and operator algebras.
Autoren/Hrsg.
Fachgebiete
- Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
- Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
- Mathematik | Informatik Mathematik Topologie Algebraische Topologie
- Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
- Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
- Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
- Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
- Mathematik | Informatik Mathematik Operations Research Graphentheorie
- Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
- Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
- Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
- Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
- Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
- Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
