Details

Autor(en) / Beteiligte

• Casazza, Peter G.,
• Shura, Thaddeus J.,

Titel

Tsirelson's space

Auflage

1st ed. 1989

Ort / Verlag

Berlin, Germany ; : Springer-Verlag,

Erscheinungsjahr

[1989]

Link zum Volltext

• SpringerLink Books - AutoHoldings

Beschreibungen/Notizen

• Bibliographic Level Mode of Issuance: Monograph
• 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).
• English
• Description based on print version record.