LEADER 03986nam 2200637 450 001 996466633303316 005 20230215152215.0 010 $a3-540-38822-2 024 7 $a10.1007/978-3-540-38822-7 035 $a(CKB)1000000000437605 035 $a(SSID)ssj0000321461 035 $a(PQKBManifestationID)12133490 035 $a(PQKBTitleCode)TC0000321461 035 $a(PQKBWorkID)10279848 035 $a(PQKB)11241555 035 $a(DE-He213)978-3-540-38822-7 035 $a(MiAaPQ)EBC3088301 035 $a(MiAaPQ)EBC6573550 035 $a(Au-PeEL)EBL6573550 035 $a(OCoLC)1255228298 035 $a(PPN)155233408 035 $a(EXLCZ)991000000000437605 100 $a20211128d2001 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aAsymptotic theory of finite dimensional normed spaces /$fVitali D. Milman, Gideon Schechtman ; with an appendix by M. Gromov 205 $aSecond edition. 210 1$aBerlin :$cSpringer,$d[2001] 210 4$dİ2001 215 $a1 online resource (XII, 160 p.) 225 1 $aLecture notes in mathematics (Springer-Verlag) ;$v1200 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-16769-2 320 $aIncludes bibliographical references and index. 327 $aThe 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. 330 $aThis book deals with the geometrical structure of finite dimensional normed spaces, as the dimension grows to infinity. This is a part of what came to be known as the Local Theory of Banach Spaces (this name was derived from the fact that in its first stages, this theory dealt mainly with relating the structure of infinite dimensional Banach spaces to the structure of their lattice of finite dimensional subspaces). Our purpose in this book is to introduce the reader to some of the results, problems, and mainly methods developed in the Local Theory, in the last few years. This by no means is a complete survey of this wide area. Some of the main topics we do not discuss here are mentioned in the Notes and Remarks section. Several books appeared recently or are going to appear shortly, which cover much of the material not covered in this book. Among these are Pisier's [Pis6] where factorization theorems related to Grothendieck's theorem are extensively discussed, and Tomczak-Jaegermann's [T-Jl] where operator ideals and distances between finite dimensional normed spaces are studied in detail. Another related book is Pietch's [Pie]. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1200. 606 $aNormed linear spaces 615 0$aNormed linear spaces. 676 $a515.732 686 $a46B20$2msc 686 $a52A20$2msc 686 $a60F10$2msc 700 $aMilman$b Vitali D.$f1939-$056003 702 $aSchechtman$b Gideon$f1947- 702 $aGromov$b Mikhael$f1943- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466633303316 996 $aAsymptotic theory of finite dimensional normed spaces$91488784 997 $aUNISA