{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/19751"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/19751","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Operators and subspaces of L(,0)","abstract":"We prove linear and non-linear lifting theorems for locally convex subspaces of $L\\sb0,$ and we give a characterization for locally bounded subspaces of $L\\sb0.$ For every closed locally convex subspace E of $L\\sb0$ and for any continuous linear operator T from $L\\sb0$ to $L\\sb0/E$ there is a continuous linear operator S from $L\\sb0$ to $L\\sb0$ such that T = QS where Q is the quotient map from $L\\sb0$ to $L\\sb0/E$.","abstract_html":"We prove linear and non-linear lifting theorems for locally convex subspaces of $L\\sb0,$ and we give a characterization for locally bounded subspaces of $L\\sb0.$ For every closed locally convex subspace E of $L\\sb0$ and for any continuous linear operator T from $L\\sb0$ to $L\\sb0/E$ there is a continuous linear operator S from $L\\sb0$ to $L\\sb0$ such that T = QS where Q is the quotient map from $L\\sb0$ to $L\\sb0/E$.","abstract_has_math":true,"creators":["Faber, Richard George"],"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":2011,"date_issued":"2011-05-07T12:17:21Z","date_published":"2011-05-07T12:17:21Z","updated_at":"2026-07-22T22:25:14Z","subjects":["Mathematics"],"languages":["eng"],"rights":["Copyright 1995 Faber, Richard George"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9601091","(UMI)AAI9601091"],"render_values":[{"text":"AAI9601091","href":null,"code":true},{"text":"(UMI)AAI9601091","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/19751","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Faber, Richard George"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:17:21Z","10000-01-01","1995"]},{"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":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1995 Faber, Richard George"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9601091","(UMI)AAI9601091","http://hdl.handle.net/2142/19751"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We prove linear and non-linear lifting theorems for locally convex subspaces of $L\\sb0,$ and we give a characterization for locally bounded subspaces of $L\\sb0.$ For every closed locally convex subspace E of $L\\sb0$ and for any continuous linear operator T from $L\\sb0$ to $L\\sb0/E$ there is a continuous linear operator S from $L\\sb0$ to $L\\sb0$ such that T = QS where Q is the quotient map from $L\\sb0$ to $L\\sb0/E$.","If X is a paracompact space and E is a closed locally convex subspace the F-space Y then for any continuous map f from X to Y/E there is a continuous map F from X to Y such that F = Qf where Q is the quotient map from Y to Y/E.","We give a characterization of locally bounded subspaces of $L\\sb0$.","Made available in DSpace on 2011-05-07T12:17:21Z (GMT). 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