03293nam 2200637 450 99646665120331620220913114752.03-540-46069-110.1007/BFb0085267(CKB)1000000000437443(SSID)ssj0000327430(PQKBManifestationID)12089434(PQKBTitleCode)TC0000327430(PQKBWorkID)10299451(PQKB)11174449(DE-He213)978-3-540-46069-5(MiAaPQ)EBC5592165(Au-PeEL)EBL5592165(OCoLC)1066195538(MiAaPQ)EBC6842679(Au-PeEL)EBL6842679(PPN)155183311(EXLCZ)99100000000043744320220913d1989 uy 0engurnn|008mamaatxtccrTsirelson's space /Peter G. Casazza and Thaddeus J. Shura1st ed. 1989.Berlin, Germany ;New York, New York :Springer-Verlag,[1989]©19891 online resource (X, 206 p.) Lecture Notes in Mathematics,0075-8434 ;1363Bibliographic Level Mode of Issuance: Monograph3-540-50678-0 Precursors 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.This 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).Lecture Notes in Mathematics,0075-8434 ;1363MathematicsBanach spacesGlobal analysis (Mathematics)Mathematics.Banach spaces.Global analysis (Mathematics)515.732Casazza Peter G.1945-55468Shura Thaddeus J.1947-MiAaPQMiAaPQMiAaPQBOOK996466651203316Tsirelson's space262239UNISA