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.
254 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
![Asymptotic Theory of Finite Dimensional Normed Spaces [1 ed.]
9780387167695, 0-387-16769-2, 3540167692](https://ebin.pub/img/200x200/asymptotic-theory-of-finite-dimensional-normed-spaces-1nbsped-9780387167695-0-387-16769-2-3540167692.jpg)
![A Primer on Hilbert Space Theory: Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups (UNITEXT for Physics) [2nd ed. 2021]
3030674169, 9783030674168](https://ebin.pub/img/200x200/a-primer-on-hilbert-space-theory-linear-spaces-topological-spaces-metric-spaces-normed-spaces-and-topological-groups-unitext-for-physics-2nd-ed-2021-3030674169-9783030674168.jpg)
![Normed Linear Spaces [3 ed.]
9780444108227, 044410822X, 9783540061489, 3540061487](https://ebin.pub/img/200x200/normed-linear-spaces-3nbsped-9780444108227-044410822x-9783540061489-3540061487.jpg)
![Asymptotic theory for econometricians [Revised]
0127466525, 9780127466521](https://ebin.pub/img/200x200/asymptotic-theory-for-econometricians-revised-0127466525-9780127466521.jpg)