1.

Record Nr.

UNISA996466651203316

Autore

Casazza Peter G. <1945->

Titolo

Tsirelson's space / / Peter G. Casazza and Thaddeus J. Shura

Pubbl/distr/stampa

Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [1989]

©1989

ISBN

3-540-46069-1

Edizione

[1st ed. 1989.]

Descrizione fisica

1 online resource (X, 206 p.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 1363

Disciplina

515.732

Soggetti

Mathematics

Banach spaces

Global analysis (Mathematics)

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di contenuto

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.

Sommario/riassunto

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).