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E-grāmata: Lipschitz Algebras (Second Edition)

(Washington Univ In St Louis, Usa)
  • Formāts: 472 pages
  • Izdošanas datums: 14-May-2018
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789814740654
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  • Formāts: 472 pages
  • Izdošanas datums: 14-May-2018
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789814740654
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'The book is very well-written by one of the leading figures in the subject. It is self-contained, includes relevant recent advances and is enriched by a large number of examples and illustrations. In addition to the general bibliography, each chapter includes a section of notes, which details the authorship of the main results, and provides useful hints for further readings. Undoubtedly, this edition will be received by researchers with the same success as the first one.'European Mathematical SocietyThis 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.
Preface v
Notation Index ix
1 Lipschitz Functions
1(34)
1.1 Classes of metric spaces
1(2)
1.2 Lipschitz functions
3(5)
1.3 Sums and products of metric spaces
8(6)
1.4 Quotients of metric spaces
14(5)
1.5 Scalar-valued Lipschitz functions
19(8)
1.6 Rademacher's theorem
27(7)
1.7 Notes
34(1)
2 Lipschitz Spaces
35(46)
2.1 Lip and Lip0 spaces
35(7)
2.2 Lip versus Lip0
42(7)
2.3 Composition maps
49(6)
2.4 Do Leeuw's map
55(4)
2.5 Lipschitz gauges
59(6)
2.6 Distortion
65(8)
2.7 Extreme points
73(5)
2.8 Notes
78(3)
3 The Predual
81(46)
3.1 The Arens-Eells space
81(5)
3.2 Examples
86(4)
3.3 The mass transfer problem
90(5)
3.4 Uniqueness of the predual
95(6)
3.5 Weak* extreme points (existence)
101(9)
3.6 Weak* extreme points (characterization)
110(8)
3.7 Isometries of Lip spaces
118(2)
3.8 Isometries of Lip0 spaces
120(4)
3.9 Notes
124(3)
4 Little Lipschitz Spaces, I
127(36)
4.1 The compact case
127(7)
4.2 The general case
134(13)
4.3 Duality
147(5)
4.4 Extensions of little Lipschitz functions
152(9)
4.5 Notes
161(2)
5 Linearization
163(24)
5.1 Linear surrogates
163(8)
5.2 Lipschitz extension constants
171(6)
5.3 Isometric embedding
177(4)
5.4 Nonseparable counterexamples
181(4)
5.5 Notes
185(2)
6 Lattice Structure
187(42)
6.1 Linear complete sublattices of Lip0(X)
187(8)
6.2 Complete bands of Lip0(X)
195(6)
6.3 Stone lattices
201(6)
6.4 Complete distributivity
207(3)
6.5 Embedding in cubes
210(6)
6.6 Lipschitz lattices
216(5)
6.7 Completely distributive Lipschitz lattices
221(6)
6.8 Notes
227(2)
7 Algebraic Structure
229(32)
7.1 Order complete subalgebras of Lip0(X)
229(6)
7.2 Order complete ideals of Lip0(X)
235(3)
7.3 Spectra
238(9)
7.4 Norm closed ideals
247(4)
7.5 Point derivations
251(2)
7.6 Spectral synthesis
253(6)
7.7 Notes
259(2)
8 Little Lipschitz Spaces, II
261(36)
8.1 Little Lipschitz sublattices
261(7)
8.2 Little Lipschitz bands
268(6)
8.3 Little Lipschitz subalgebras
274(3)
8.4 Little Lipschitz ideals
277(3)
8.5 Holder cubes
280(6)
8.6 Finite dimensional Holder spaces
286(8)
8.7 Notes
294(3)
9 Measurable Metrics
297(56)
9.1 Localizable measure spaces
297(3)
9.2 Measurable pseudometrics
300(5)
9.3 Measurable relations
305(8)
9.4 Lipschitz functions
313(9)
9.5 Lipschitz spaces
322(9)
9.6 Lipschitz gauges
331(5)
9.7 Algebra and lattice structure
336(12)
9.8 Lipschitz lattices
348(4)
9.9 Notes
352(1)
10 Derivations
353(58)
10.1 L∞-modules
353(14)
10.2 The derivation theorem
367(10)
10.3 The exterior derivative
377(8)
10.4 Examples
385(6)
10.5 Locally controlled oscillation
391(4)
10.6 Dirichlet forms
395(8)
10.7 The Sierpinski gasket
403(4)
10.8 Wiener spaces
407(2)
10.9 Notes
409(2)
11 Quantum Metrics
411(36)
11.1 Quantum relations
411(8)
11.2 Quantum metrics
419(10)
11.3 Examples
429(7)
11.4 Spectral Lipschitz numbers
436(6)
11.5 Commutation Lipschitz numbers
442(4)
11.6 Notes
446(1)
Bibliography 447(6)
Subject, Index 453