Tsirelson's space
By: Peter G. Casazza, Thaddeus J. Shura ; with an appendix by J. Baker, O. Slotterbeck, and R. Aron.
Contributors: Shura, Thaddeus J., 1947-
Series: Lecture notes in mathematics ;; 1363; Lecture notes in mathematics (Springer-Verlag) ;; 1363.
Publisher: Springer-Verlag
Published: 1989
Place of publication: Berlin; New York
Language: eng
Number of pages: 204
Subjects: Banach spaces.
Description: 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).
Notes: Includes bibliographies and index.