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