Tsirelson’s Space
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ISBN-13:
9783540506782
Veröffentl:
1989
Einband:
Paperback
Erscheinungsdatum:
11.01.1989
Seiten:
216
Autor:
Thaddeus J. Shura
Gewicht:
335 g
Format:
235x155x12 mm
Serie:
1363, Lecture Notes in Mathematics
Sprache:
Englisch
Beschreibung:
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 "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.
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