Author	Casazza, Peter G. author
Title	Tsirelson's Space [electronic resource] : With an Appendix by J. Baker, O. Slotterbeck and R. Aron / by Peter G. Casazza, Thaddeus J. Shura
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1989
Connect to	http://dx.doi.org/10.1007/BFb0085267
Descript	X, 206 p. online resource

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)

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 โblockingโ 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

1. Mathematics
2. Mathematical analysis
3. Analysis (Mathematics)
4. Mathematics
5. Analysis