Weaver N. — Lipschitz Algebras :: Электронная библиотека попечительского совета мехмата МГУ

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Weaver N. — Lipschitz Algebras

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Название: Lipschitz Algebras

Автор: Weaver N.

Аннотация:

The Lipschitz algebras Lp(M), for M a complete metric space, are quite analogous to the spaces C() and L(X), for a compact Hausdorff space and X a -finite measure space. Although the Lipschitz algebras have not been studied as thoroughly as these better-known cousins, it is becoming increasingly clear that they play a fundamental role in functional analysis, and are also useful in many applications, especially in the direction of metric geometry. This book gives a comprehensive treatment of (what is currently known about) the beautiful theory of these algebras.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 223

Добавлена в каталог: 03.04.2008

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Предметный указатель

$(\delta, \epsilon)$ -flat function      80
$L^{\infty}$ -bimodule      190
$L^{\infty}$ -derivation      190
$L^{\infty}$ -diffusion form      196
$L^{\infty}$ -module      202
$\alpha$ -dilation      68
1-connected metric space      62
Aligned extreme points      65
Archemedian vector lattice      151
Arens — Eells space      38
Axiom of Choice      4
Bade, Curtis, and Dales      136
Banach      30
Banach bundle      203
Banach lattice      147
Banach manifold      206
Base point      2
Base point-preserving map      3
Benyamini and Wojtaszczyk      98
Beurling algebra      117
bi-Lipschitz map      3
Bimodule      34
Bonic, Frampton, and Tromba      99
Carrier space      112
Choice function      140
Ciesielski      99
Clopen subset      137
Complete lattice      137
Complete ring of subsets      137
Complete sublattice      137
Completely distributive lattice      140
Composition map      28
Concave metric space      51
Cost of a transfer plan      44
de Leeuw      33 99
de Leeuw's map      34 176
Decomposition of $\beta\tilde{X}-\tilde{X}$       55
Derivation      34
Diameter of a metric space      1
Dilation      25
Dirichlet form      196
Distributive law      141
Double duality      83
Embedding of complete lattices      137
Equicontinuous Banach algebra      116
Essential containment      162
Essential range      168
Essential union      163
Evaluation functional      25
Existence of an optimal transfer plan      48
Exterior derivative      203
Finitely decomposable measure space      162
Finsler structure      203 211
Four-element condition      19
Frechet      30
Gelfand transform      116
Glaeser      99 136
Glueing lemma, lack of      5
Goedel      4
Gradient vector field      192
Hausdorff complete lattice      143
Hedberg      136
Helly's theorem      19
Hilbert cube      98 205
Hildert module      193 203
Hoelder map      3
Hoelder metric space      2
Intrinsic metric      201 210
Jenkins      99
Johnson      99
Join      137
k-edge      87
k-vertex      86
Kantorovich — Rubenstein space      45
Kirszbraun's theorem      19
Krein — Smulian Theorem      34
Lattice carrier space      149
Lattice Urysohn's lemma      144
Lattice-generation      165
Lip-derivation      202
Lipschitz functional calculi      74 117 198

Lipschitz lattice      150
Lipschitz manifold      204
Lipschitz map      3
Lipschitz norm      19
Lipschitz number      3 169
Little Lipschitz function      73
Little Lipschitz space      74
Little metric Banach — Stone theorems      86
Little metric Stone — Weierstrass theorem      118
Little metric Tietze extension theorem      81
Local linear functional      133
Lying over p      128
Mass transfer problem      43
Measurable 1-forms      203
Measurable Lipschitz lattice      185
Measurable metric (space)      164
Measurable pseudometric (space)      164
Measurable vector fields      202
Meet      137
Metric Banach — Stone theorems      66 68
Metric embedding in cubes      7
Metric Stone — Cech compactification      115
Metric Stone — Weierstrass theorem      105 179
Metric Tietze extension theorem      16 175
Metric Urysohn's lemma      4
Molecule      38
Myers      136
Non-reflexivity of $Lip_{0}(X)$       57
Noncommutative Lipschitz algebra      208
Noncommutative tori      208
Normal 0,1-lattice homomorphism      140
Normal lattice homomorphism      137 149 152
Normal linear functional      36
Normal linear map      102 183
Normed vector lattice      147
Open mapping theorem      79
Order complete subspace      102
Order dual      185
Ordered Banach space      185
Ordered vector space      146
Peaking function      49
Point derivation      128
Pointed metric space      2
Pointwise (pseudo)metric      166
Positive linear functional      182
Preorder      182
Preordered Banach space      182
Primary ideal      130
Product of metric spaces      6
Pure state      113
Quasi-isometry      3
Quotient of a metric space      11
Radon — Nikodym property      71
Raney      159
Raney's theorem      145
Rectifiable set      205
Relationship between Lip and $Lip_{0}$       25
Respect (of a function)      10
Respect (of a pseudometric)      10
Riesz law      147
Self-adjoint subspace      102
Sierpinski carpet      204
Simple extreme point      63
Source of v      89
Spectral synthesis      135
State of $Lip_{0}(X)$       112 136
Stone lattice      137
Stone — Cech compactification      36
Sub-Riemannian manifold      205
Transfer plan      43 44
Unbounded Fredholm module      208
Uniform separation of points      77 102
Uniqueness of the predual      40
Universal property of AE(X)      41
Upper subset      138
Vector lattice      146
W*-bimodule      207
W*-derivation      207
Waelbroeck      136
Weak Banach algebra      101
Weak* extreme point      49

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