Tsirelson's Space
(Sprache: Englisch)
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,...
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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).
Inhaltsverzeichnis zu „Tsirelson's Space “
- 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 ätn ü
- 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
- Appendices
- Index
Bibliographische Angaben
- Autoren: Peter G. Casazza , Thaddeus J. Shura
- 1989, 1989, 206 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Mitarbeit: Baker, John
- Verlag: Springer
- ISBN-10: 3540506780
- ISBN-13: 9783540506782
- Erscheinungsdatum: 11.01.1989
Sprache:
Englisch
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