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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis
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Amenability (Paperback, 2nd ed.)
Loot Price: R3,285
Discovery Miles 32 850
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Amenability (Paperback, 2nd ed.)
Series: Mathematical Surveys and Monographs
Expected to ship within 12 - 17 working days
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The subject of amenability has its roots in the work of Lebesgue at
the turn of the century. In the 1940s, the subject began to shift
from finitely additive measures to means. This shift is of
fundamental importance, for it makes the substantial resources of
functional analysis and abstract harmonic analysis available to the
study of amenability. The ubiquity of amenability ideas and the
depth of the mathematics involved points to the fundamental
importance of the subject. This book presents a comprehensive and
coherent account of amenability as it has been developed in the
large and varied literature during this century. The book has a
broad appeal, for it presents an account of the subject based on
harmonic and functional analysis. In addition, the analytic
techniques should be of considerable interest to analysts in all
areas.In addition, the book contains applications of amenability to
a number of areas: combinatorial group theory, semigroup theory,
statistics, differential geometry, Lie groups, ergodic theory,
cohomology, and operator algebras. The main objectives of the book
are to provide an introduction to the subject as a whole and to go
into many of its topics in some depth. The book begins with an
informal, nontechnical account of amenability from its origins in
the work of Lebesgue.The initial chapters establish the basic
theory of amenability and provide a detailed treatment of
invariant, finitely additive measures (i.e., invariant means) on
locally compact groups. The author then discusses amenability for
Lie groups, 'almost invariant' properties of certain subsets of an
amenable group, amenability and ergodic theorems, polynomial
growth, and invariant mean cardinalities. Also included are
detailed discussions of the two most important achievements in
amenability in the 1980s: the solutions to von Neumann's conjecture
and the Banach-Ruziewicz Problem. The main prerequisites for this
book are a sound understanding of undergraduate-level mathematics
and a knowledge of abstract harmonic analysis and functional
analysis. The book is suitable for use in graduate courses, and the
lists of problems in each chapter may be useful as student
exercises.
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