Asymptotic Theory of Finite Dimensional Normed Spaces [1 ed.] 9780387167695, 0-387-16769-2, 3540167692
This book deals with the geometrical structure of finite dimensional normed spaces, as the dimension grows to infinity.
255 97 769KB
English Pages 160 [163] Year 1986
Table of contents :
Front Matter....Pages I-X
Preliminaries....Pages 1-4
The Isoperimetric Inequality on S n−1 and Some Consequences....Pages 5-8
Finite Dimensional Normed Spaces, Preliminaries....Pages 9-11
Almost Euclidean Subspaces of A Normed Space....Pages 12-18
Almost Euclidean Subspaces of ℓ {p} n Spaces, of General n -Dimensional Normed Spaces, and of Quotient of n -Dimensional Spaces....Pages 19-26
Levy Families....Pages 27-32
Martingales....Pages 33-41
Embedding ℓ p m into ℓ 1 n ....Pages 42-50
Type and Cotype of Normed Spaces, and Some Simple Relations with Geometrical Properties....Pages 51-59
Additional Applications of Levy Families in the Theory of Finite Dimensional Normed Spaces....Pages 60-68
Ramsey’s Theorem with Some Applications to Normed Spaces....Pages 69-76
Krivine’s Theorem....Pages 77-84
The Maurey-Pisier Theorem....Pages 85-97
The Rademacher Projection....Pages 98-105
Projections on Random Euclidean Subspaces of Finite Dimensional Normed Spaces....Pages 106-113
Back Matter....Pages 114-156
Front Matter....Pages I-X
Preliminaries....Pages 1-4
The Isoperimetric Inequality on S n−1 and Some Consequences....Pages 5-8
Finite Dimensional Normed Spaces, Preliminaries....Pages 9-11
Almost Euclidean Subspaces of A Normed Space....Pages 12-18
Almost Euclidean Subspaces of ℓ {p} n Spaces, of General n -Dimensional Normed Spaces, and of Quotient of n -Dimensional Spaces....Pages 19-26
Levy Families....Pages 27-32
Martingales....Pages 33-41
Embedding ℓ p m into ℓ 1 n ....Pages 42-50
Type and Cotype of Normed Spaces, and Some Simple Relations with Geometrical Properties....Pages 51-59
Additional Applications of Levy Families in the Theory of Finite Dimensional Normed Spaces....Pages 60-68
Ramsey’s Theorem with Some Applications to Normed Spaces....Pages 69-76
Krivine’s Theorem....Pages 77-84
The Maurey-Pisier Theorem....Pages 85-97
The Rademacher Projection....Pages 98-105
Projections on Random Euclidean Subspaces of Finite Dimensional Normed Spaces....Pages 106-113
Back Matter....Pages 114-156
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