TY  - BOOK
AU  - Casazza,Peter G.
AU  - Shura,Thaddeus J.
ED  - SpringerLink (Online service)
TI  - Tsirelson's Space: With an Appendix by J. Baker, O. Slotterbeck and R. Aron 
T2  - Lecture Notes in Mathematics,
SN  - 9783540460695
AV  - QA299.6-433 
U1  - 515 23
PY  - 1989///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Global analysis (Mathematics)
KW  - Analysis
N1  - 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
N2  - 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)
UR  - http://dx.doi.org/10.1007/BFb0085267
ER  -