Banach Spaces from Barriers in High Dimensional Ellentuck Spaces

Author

Gabriel Girón-Garnica, University of DenverFollow

Date of Award

1-1-2017

Document Type

Dissertation

Degree Name

Ph.D.

Organizational Unit

College of Natual Science and Mathematics, Mathematics

First Advisor

Álvaro Arias, Ph.D.

Keywords

Banach space theory, Infinite combinatorics

Abstract

We construct new Banach spaces using barriers in high dimensional Ellentuck spaces following the classical framework under which a Tsirelson type norm is defined from a barrier in Ellentuck space. It is shown that these spaces contain arbitrary large copies of lⁿ_infinity and specific block subspaces isomorphic to l_p. We also prove that they are l_p-saturated and not isomorphic to each other. Finally, a study of alternative norms for our spaces is presented.

Publication Statement

Copyright is held by the author. User is responsible for all copyright compliance.

Rights Holder

Gabriel Girón-Garnica

Provenance

Received from ProQuest

File Format

application/pdf

Language

en

File Size

88 p.

Recommended Citation

Girón-Garnica, Gabriel, "Banach Spaces from Barriers in High Dimensional Ellentuck Spaces" (2017). Electronic Theses and Dissertations. 1310.
https://digitalcommons.du.edu/etd/1310

Copyright date

2017

Discipline

Mathematics, Theoretical Mathematics