This is the standard reference on algebras of Lipschitz functions, written by the leading figure in the field. The second edition includes new chapters on nonlinear Banach space geometry, differentiability in metric measure spaces, and quantum metrics. This latest material reflects the importance of spaces of Lipschitz functions in a diverse range of current research directions. Every functional analyst should have some knowledge of this subject.
Contents: Lipschitz FunctionsLipschitz Spaces and Their PredualsLittle Lipschitz SpacesBanach Space GeometryLipschitz LatticesLipschitz AlgebrasMeasurable MetricsThe Exterior DerivativeDerivationsQuantum Metrics
Readership: Graduate students and specialists in functional analysis.
Keywords: Lipschitz Algebras;Lipschitz Spaces;Lipschitz Functions;Metric Spaces;Functional Analysis;Banach Spaces;Arens-Eells Spaces;Lipschitz-Free Spaces;Metric Measure Spaces;Lattice Theory;Dirichlet FormsReview:
Reviews of the First Edition:
"This nice little volume attempts, with considerable success, to place spaces and algebras of Lipschitz functions in functional analysis alongside their more familiar cousins whose elements are continuous or measurable functions of one sort or another. Most readers will discover that its subject is richer than they imagined, and that, notwithstanding the author's engaging style, it can be quite difficult."Mathematical Reviews
"The book is clearly written and contains a wealth of material on spaces of Lipschitz functions, available for the first time in book form. It is fairly self-contained, accessible to students acquainted with the basics of measure theory and functional analysis. The open problems, posed in various places in the book, open new research opportunities for the diligent reader."Studia Universitatis Babes-Bolyai, Series Mathematica
Key Features: The only in-depth treatment of a topic of wide and growing interest. Since the publication of the first edition 16 years ago, Lipschitz algebras have emerged as a centrally important tool in a range of current research areasNot only is the author responsible for large parts of the basic theory of these algebras, he has also been deeply involved in recent developments which apply this theory in other areasThe book is clearly and carefully written, with a wealth of examples which illuminate the abstract theory