LEADER 03293nam 2200637 450 001 996466651203316 005 20220913114752.0 010 $a3-540-46069-1 024 7 $a10.1007/BFb0085267 035 $a(CKB)1000000000437443 035 $a(SSID)ssj0000327430 035 $a(PQKBManifestationID)12089434 035 $a(PQKBTitleCode)TC0000327430 035 $a(PQKBWorkID)10299451 035 $a(PQKB)11174449 035 $a(DE-He213)978-3-540-46069-5 035 $a(MiAaPQ)EBC5592165 035 $a(Au-PeEL)EBL5592165 035 $a(OCoLC)1066195538 035 $a(MiAaPQ)EBC6842679 035 $a(Au-PeEL)EBL6842679 035 $a(PPN)155183311 035 $a(EXLCZ)991000000000437443 100 $a20220913d1989 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aTsirelson's space /$fPeter G. Casazza and Thaddeus J. Shura 205 $a1st ed. 1989. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer-Verlag,$d[1989] 210 4$dİ1989 215 $a1 online resource (X, 206 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1363 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-50678-0 327 $aPrecursors of the Tsirelson construction -- The Figiel-Johnson construction of Tsirelson's space -- Block basic sequences in Tsirelson's space -- Bounded linear operators on T and the ?blocking? principle -- Subsequences of the unit vector basis of Tsirelson's space -- Modified Tsirelson's Space: TM -- Embedding Theorems about T and T -- Isomorphisms between subspaces of Tsirelson's space which are spanned by subsequences of -- Permutations of the unit vector basis of Tsirelson's space -- Unconditional bases for complemented subspaces of Tsirelson's space -- Variations on a Theme -- Some final comments. 330 $aThis monograph provides a structure theory for the increasingly important Banach space discovered by B.S. Tsirelson. The basic construction should be accessible to graduate students of functional analysis with a knowledge of the theory of Schauder bases, while topics of a more advanced nature are presented for the specialist. Bounded linear operators are studied through the use of finite-dimensional decompositions, and complemented subspaces are studied at length. A myriad of variant constructions are presented and explored, while open questions are broached in almost every chapter. Two appendices are attached: one dealing with a computer program which computes norms of finitely-supported vectors, while the other surveys recent work on weak Hilbert spaces (where a Tsirelson-type space provides an example). 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1363 606 $aMathematics 606 $aBanach spaces 606 $aGlobal analysis (Mathematics) 615 0$aMathematics. 615 0$aBanach spaces. 615 0$aGlobal analysis (Mathematics) 676 $a515.732 700 $aCasazza$b Peter G.$f1945-$055468 702 $aShura$b Thaddeus J.$f1947- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466651203316 996 $aTsirelson's space$9262239 997 $aUNISA