Casazza, Peter G.
Tsirelson's Space With an Appendix by J. Baker, O. Slotterbeck and R. Aron / [electronic resource] : by Peter G. Casazza, Thaddeus J. Shura. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1989. - X, 206 p. online resource. - Lecture Notes in Mathematics, 1363 0075-8434 ; . - Lecture Notes in Mathematics, 1363 .
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).
9783540460695
10.1007/BFb0085267 doi
Mathematics.
Global analysis (Mathematics).
Mathematics.
Analysis.
QA299.6-433
515
Tsirelson's Space With an Appendix by J. Baker, O. Slotterbeck and R. Aron / [electronic resource] : by Peter G. Casazza, Thaddeus J. Shura. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1989. - X, 206 p. online resource. - Lecture Notes in Mathematics, 1363 0075-8434 ; . - Lecture Notes in Mathematics, 1363 .
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).
9783540460695
10.1007/BFb0085267 doi
Mathematics.
Global analysis (Mathematics).
Mathematics.
Analysis.
QA299.6-433
515