Banach Spaces on Infinitely Branching Trees

Author

Annette B. Locke, University of DenverFollow

Date of Award

11-1-2009

Document Type

Dissertation

Degree Name

Ph.D.

Organizational Unit

College of Natual Science and Mathematics

First Advisor

James N. Hagler, Ph.D.

Second Advisor

Alvaro Arias

Third Advisor

Stanley Gudder

Fourth Advisor

Frederic Latremoliere

Fifth Advisor

Susan E. Sadler

Keywords

Banach space theory, Infinite combinatorics

Abstract

An example of a Banach space, X_∞, with a nonseparable dual such that l₁ does not imbed in X_∞ is investigated. Not every weakly null sequence has a subsequence equivalent to the usual basis of c₀, but c₀ imbeds in many subspaces of X_∞. The space l₁ does imbed in X_∞^∗, the dual space of X_∞, yet weakly converging sequences in X_∞^∗ need not converge in norm.

Publication Statement

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

Rights Holder

Annette B. Locke

Provenance

Received from ProQuest

File Format

application/pdf

Language

en

File Size

117 p.

Recommended Citation

Locke, Annette B., "Banach Spaces on Infinitely Branching Trees" (2009). Electronic Theses and Dissertations. 377.
https://digitalcommons.du.edu/etd/377

Copyright date

2009

Discipline

Mathematics