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Tables of Contents for Lipschitz Algebras
Chapter/Section Title
Page #
Page Count
Preface
vii
Lipschitz Spaces
1
32
Metric spaces
1
2
Lipschitz functions
3
3
Products of metric spaces
6
3
Quotients of metric spaces
9
4
Scalar-valued Lipschitz functions
13
6
Lipschitz spaces
19
5
Lip and Lip0
24
4
Composition maps
28
2
Notes
30
3
The Predual
33
40
De Leeuw's map
33
5
The Arens-Eells space
38
5
The mass transfer problem
43
6
Weak* extreme points (existence)
49
5
Weak* extreme points (characterization)
54
7
Isometries of Lip spaces
61
6
Isometries of Lip0 spaces
67
3
Notes
70
3
Little Lipschitz Spaces
73
28
lip0(X)
73
4
Extensions of little Lipschitz functions
77
5
Double duality
82
4
Cubes in RN
86
6
Compact subsets of RN
92
7
Notes
99
2
Lipschitz Algebras
101
36
Order complete subalgebras
101
6
Order complete ideals
107
5
Carrier spaces
112
5
Little Lipschitz subalgebras
117
6
Little Lipschitz ideals
123
2
Norm closed ideals
125
3
Point derivations
128
2
Spectral synthesis
130
6
Notes
136
1
Lipschitz Lattices
137
24
Stone lattices
137
3
Completely distributive lattices
140
3
Raney's theorem
143
3
Lip(X) as a vector lattice
146
4
Lipschitz lattices, I
150
3
Lipschitz lattices, II
153
6
Notes
159
2
Measurable Lipschitz Algebras
161
28
Measurable metrics
161
7
Lip(X,μ), I
168
8
Lip(X,μ), II
176
5
Measurable Lipschitz lattices
181
6
Notes
187
2
Derivations
189
24
Examples
189
8
The derivation theorem
197
4
The exterior derivative
201
5
Noncommutative metrics
206
4
Notes
210
3
Table of Symbols
213
2
Bibliography
215
6
Index
221