{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71250"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71250","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Uniform Convergence of Operators and Grothendieck Spaces With the Dunford-Pettis Property","abstract":"A theorem of D. W. Dean states that all Grothendieck spaces with the Dunford-Pettis property fail to admit Schauder decompositions. Similar results of H. P. Lotz concern the uniform convergence of ergodic operators and semi-groups of operators. This thesis considers extensions of these results to wider classes of Banach spaces.","abstract_html":"A theorem of D. W. Dean states that all Grothendieck spaces with the Dunford-Pettis property fail to admit Schauder decompositions. Similar results of H. P. Lotz concern the uniform convergence of ergodic operators and semi-groups of operators. This thesis considers extensions of these results to wider classes of Banach spaces.","abstract_has_math":false,"creators":["Leung, Denny Ho-Hon"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T06:18:17Z","date_published":"2014-12-16T06:18:17Z","updated_at":"2026-07-22T22:26:04Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8711827"],"render_values":[{"text":"(UMI)AAI8711827","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71250","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Leung, Denny Ho-Hon"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T06:18:17Z","10000-01-01","1987"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/71250","(UMI)AAI8711827"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A theorem of D. W. Dean states that all Grothendieck spaces with the Dunford-Pettis property fail to admit Schauder decompositions. Similar results of H. P. Lotz concern the uniform convergence of ergodic operators and semi-groups of operators. This thesis considers extensions of these results to wider classes of Banach spaces.","We say that a Banach space E has the surjective Dunford-Pettis property if every operator from E onto a reflexive Banach space maps weakly compact sets onto norm compact sets. The main result can now be stated.","Theorem. Let E be a Grothendieck space with the surjective Dunford-Pettis property, then (1) The space E admits no Schauder decompositions; (2) Every strongly ergodic operator T on E with (VBAR)(VBAR)T('n)/n(VBAR)(VBAR) (--->) 0 is uniformly ergodic; and (3) Every strongly continuous semi-group of operators (T(,t))(,t(GREATERTHEQ)0) on E is uniformly continuous.","Examples are presented to distinguish the surjective Dunford-Pettis property from the closely related Dunford-Pettis property.","Made available in DSpace on 2014-12-16T06:18:17Z (GMT). No. of bitstreams: 1 8711827.pdf: 2402542 bytes, checksum: 65d828d7b411ddbc74ef602599d6825f (MD5) Previous issue date: 1987","Embargo set by: Seth Robbins for item 71416 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","89 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987."]},{"key":"dc:title","label":"Title","values":["Uniform Convergence of Operators and Grothendieck Spaces With the Dunford-Pettis Property"]}]}],"canonical_facts":{"dc:creator":["Leung, Denny Ho-Hon"],"dc:date":["2014-12-16T06:18:17Z","10000-01-01","1987"],"dc:description":["A theorem of D. W. Dean states that all Grothendieck spaces with the Dunford-Pettis property fail to admit Schauder decompositions. Similar results of H. P. Lotz concern the uniform convergence of ergodic operators and semi-groups of operators. This thesis considers extensions of these results to wider classes of Banach spaces.","We say that a Banach space E has the surjective Dunford-Pettis property if every operator from E onto a reflexive Banach space maps weakly compact sets onto norm compact sets. The main result can now be stated.","Theorem. Let E be a Grothendieck space with the surjective Dunford-Pettis property, then (1) The space E admits no Schauder decompositions; (2) Every strongly ergodic operator T on E with (VBAR)(VBAR)T('n)/n(VBAR)(VBAR) (--->) 0 is uniformly ergodic; and (3) Every strongly continuous semi-group of operators (T(,t))(,t(GREATERTHEQ)0) on E is uniformly continuous.","Examples are presented to distinguish the surjective Dunford-Pettis property from the closely related Dunford-Pettis property.","Made available in DSpace on 2014-12-16T06:18:17Z (GMT). No. of bitstreams: 1 8711827.pdf: 2402542 bytes, checksum: 65d828d7b411ddbc74ef602599d6825f (MD5) Previous issue date: 1987","Embargo set by: Seth Robbins for item 71416 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","89 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987."],"dc:identifier":["http://hdl.handle.net/2142/71250","(UMI)AAI8711827"],"dc:subject":["Mathematics"],"dc:title":["Uniform Convergence of Operators and Grothendieck Spaces With the Dunford-Pettis Property"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:04Z"}