(Ebook) Lipschitz algebras 2nd Edition by Nik Weaver ISBN 9814740632 9789814740630

(Ebook) Lipschitz algebras 2nd Edition by Nik Weaver ISBN 9814740632 9789814740630

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ISBN 10: 9814740632 
ISBN 13: 9789814740630
Author: Nik Weaver

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.

(Ebook) Lipschitz algebras 2nd Table of contents:

1. Lipschitz Functions
1.1. Classes of metric spaces
1.2. Lipschitz functions
1.3. Sums and products of metric spaces
1.4. Quotients of metric spaces
1.5. Scalar-valued Lipschitz functions
1.6. Rademacher’s theorem
1.7. Notes
2. Lipschitz Spaces
2.1. Lip and Lip0 spaces
2.2. Lip versus Lip0
2.3. Composition maps
2.4. De Leeuw’s map
2.5. Lipschitz gauges
2.6. Distortion
2.7. Extreme points
2.8. Notes
3. The Predual
3.1. The Arens-Eells space
3.2. Examples
3.3. The mass transfer problem
3.4. Uniqueness of the predual
3.5. Weak∗ extreme points (existence)
3.6. Weak∗ extreme points (characterization)
3.7. Isometries of Lip spaces
3.8. Isometries of Lip0 spaces
3.9. Notes
4. Little Lipschitz Spaces, I
4.1. The compact case
4.2. The general case
4.3. Duality
4.4. Extensions of little Lipschitz functions
4.5. Notes
5. Linearization
5.1. Linear surrogates
5.2. Lipschitz extension constants
5.3. Isometric embedding
5.4. Nonseparable counterexamples
5.5. Notes
6. Lattice Structure
6.1. Linear complete sublattices of Lip0(X)
6.2. Complete bands of Lip0(X)
6.3. Stone lattices
6.4. Complete distributivity
6.5. Embedding in cubes
6.6. Lipschitz lattices
6.7. Completely distributive Lipschitz lattices
6.8. Notes
7. Algebraic Structure
7.1. Order complete subalgebras of Lip0(X)
7.2. Order complete ideals of Lip0(X)
7.3. Spectra
7.4. Norm closed ideals
7.5. Point derivations
7.6. Spectral synthesis
7.7. Notes
8. Little Lipschitz Spaces, II
8.1. Little Lipschitz sublattices
8.2. Little Lipschitz bands
8.3. Little Lipschitz subalgebras
8.4. Little Lipschitz ideals
8.5. Hölder cubes
8.6. Finite dimensional H¨older spaces
8.7. Notes
9. Measurable Metrics
9.1. Localizable measure spaces
9.2. Measurable pseudometrics
9.3. Measurable relations
9.4. Lipschitz functions
9.5. Lipschitz spaces
9.6. Lipschitz gauges
9.7. Algebra and lattice structure
9.8. Lipschitz lattices
9.9. Notes
10. Derivations
10.1 L∞-modules
10.2 The derivation theorem
10.3 The exterior derivative
10.4 Examples
10.5 Locally controlled oscillation
10.6 Dirichlet forms
10.7 The Sierpinski gasket
10.8 Wiener spaces
10.9 Notes
11. Quantum Metrics
11.1 Quantum relations
11.2 Quantum metrics
11.3 Examples
11.4 Spectral Lipschitz numbers
11.5 Commutation Lipschitz numbers
11.6 Notes
Bibliography

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