Date of Award
James N. Hagler, Ph.D.
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.
Locke, Annette B., "Banach Spaces on Infinitely Branching Trees" (2009). Electronic Theses and Dissertations. 377.
Received from ProQuest
Annette B. Locke