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.
","abstract_html":"<p>An example of a Banach space, X<sub>∞</sub>, with a nonseparable dual such that <em>l</em><sub>1</sub> does not imbed in X<sub>∞</sub> is investigated. Not every weakly null sequence has a subsequence equivalent to the usual basis of c<sub>0</sub>, but c<sub>0</sub> imbeds in many subspaces of X<sub>∞</sub>. The space <em>l</em><sub>1</sub> does imbed in X<sub>∞</sub><sup>∗</sup>, the dual space of X<sub>∞</sub>, yet weakly converging sequences in X<sub>∞</sub><sup>∗</sup> need not converge in norm.</p>","abstract_has_math":false,"creators":["Locke, Annette B."],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["James N. Hagler, Ph.D.","Alvaro Arias","Stanley Gudder","Frederic Latremoliere","Susan E. Sadler"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009-11-01T07:00:00Z","date_published":"2009-11-01T07:00:00Z","updated_at":"2026-07-24T02:03:26Z","subjects":["Banach space theory","Infinite combinatorics","Mathematics","Physical Sciences and Mathematics"],"languages":["en"],"rights":["Copyright is held by the author. User is responsible for all copyright compliance.
"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.du.edu/etd/377","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["James N. Hagler, Ph.D.","Alvaro Arias","Stanley Gudder","Frederic Latremoliere","Susan E. Sadler"]},{"key":"dc:creator","label":"Author","values":["Locke, Annette B."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2001-01-01T08:00:00Z"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Banach space theory","Infinite combinatorics","Mathematics","Physical Sciences and Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright is held by the author. User is responsible for all copyright compliance.
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"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Banach Spaces on Infinitely Branching Trees"]}]}],"canonical_facts":{"dc:contributor":["James N. Hagler, Ph.D.","Alvaro Arias","Stanley Gudder","Frederic Latremoliere","Susan E. Sadler"],"dc:creator":["Locke, Annette B."],"dc:date.available":["2001-01-01T08:00:00Z"],"dc:description.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.
"],"dc:format":["application/pdf"],"dc:identifier":["https://digitalcommons.du.edu/etd/377"],"dc:language":["en"],"dc:rights":["Copyright is held by the author. User is responsible for all copyright compliance.
"],"dc:subject":["Banach space theory","Infinite combinatorics","Mathematics","Physical Sciences and Mathematics"],"dc:title":["Banach Spaces on Infinitely Branching Trees"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T02:03:26Z"}