Tsirelson's Space [electronic resource] : With an Appendix by J. Baker, O. Slotterbeck and R. Aron / by Peter G. Casazza, Thaddeus J. Shura.

By: Casazza, Peter G [author.]Contributor(s): Shura, Thaddeus J [author.] | SpringerLink (Online service)Material type: TextTextSeries: Lecture Notes in Mathematics ; 1363Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1989Description: X, 206 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540460695Subject(s): Mathematics | Global analysis (Mathematics) | Mathematics | AnalysisAdditional physical formats: Printed edition:: No titleDDC classification: 515 LOC classification: QA299.6-433Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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).
Item type: E-BOOKS
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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).

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