Properties and Legacies of Tsirelson Space

Tsirelson space is a reflexive, separable Banach space constructed by Boris Tsirelson to be the first example of a Banach space that does not contain an isomorphic copy of the sequence spaces c_0 or l_p for 1\leqslant p<infinity. We begin with the construction of the classical sequence spaces c_0 and l_p for 1\leqslant p<infinity by taking the completion of c_00 with respect to their norms. The proofs of non-embedding of various sequence spaces into Schreier space and Baernstein space then prepare us for the main result: the proof of the non-embedding of c_0 and l_p from 1\leqslant p< infinity in Tsirelson space. We close by discussing further properties of Tsirelson space, including reflexivity and distortability.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematical Sciences

Year dc:date.available

2013

Author dc:creator

• Hoeft, Alexandra

Contributors dc:contributor

• Kevin Beanland

• Functional Analysis
• Physical Sciences and Mathematics

Statement dc:rights

• © The Author

Identifier

https://scholarscompass.vcu.edu/etd/553

OAI identifier oai:identifier

oai:scholarscompass.vcu.edu:etd-1552