Asymptotic theory of finite dimensional normed spaces

Vitali D. Milman, Gideon Schechtman ; with an appendix by M. Gromov

Vol. 1200 of the LNM series deals with the geometrical structure of finite dimensional normed spaces. One of the main topics is the estimation of the dimensions of euclidean and l^n p spaces which nicely embed into diverse finite-dimensional normed spaces. An essential method here is the concentration of measure phenomenon which is closely related to large deviation inequalities in Probability on the one hand, and to isoperimetric inequalities in Geometry on the other. The book contains also an appendix, written by M. Gromov, which is an introduction to isoperimetric inequalities on riemannian manifolds. Only basic knowledge of Functional Analysis and Probability is expected of the reader. The book can be used (and was used by the authors) as a text for a first or second graduate course. The methods used here have been useful also in areas other than Functional Analysis (notably, Combinatorics).

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  • The Concentration of Measure Phenomenon in the Theory of Normed Spaces.- Preliminaries.- The Isoperimetric Inequality on Sn?1 and Some Consequences.- Finite Dimensional Normed Spaces, Preliminaries.- Almost Euclidean Subspaces of A Normed Space.- Almost Euclidean Subspaces of ?{p}n Spaces, of General n-Dimensional Normed Spaces, and of Quotient of n-Dimensional Spaces.- Levy Families.- Martingales.- Embedding ?pm into ?1n.- Type and Cotype of Normed Spaces, and Some Simple Relations with Geometrical Properties.- Additional Applications of Levy Families in the Theory of Finite Dimensional Normed Spaces.- Type and Cotype of Normed Spaces.- Ramsey's Theorem with Some Applications to Normed Spaces.- Krivine's Theorem.- The Maurey-Pisier Theorem.- The Rademacher Projection.- Projections on Random Euclidean Subspaces of Finite Dimensional Normed Spaces.

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書名 Asymptotic theory of finite dimensional normed spaces
著作者等 Milman, Vitali D.
Schechtman, Gideon
Schechtman G.
シリーズ名 Lecture notes in mathematics
出版元 Springer-Verlag
刊行年月 1986
版表示 1st ed. 1986. Corr. 2nd printing 2001
ページ数 viii, 156 p.
大きさ 25 cm
ISBN 0387167692
NCID BA00223257
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言語 英語
出版国 ドイツ

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