{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/19279"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/19279","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Complemented subspaces of weakL(1)","abstract":"The Banach envelope of $weakL\\sp1$ (denoted $wL\\sb{\\1})$ is a sort of universal Banach space for separable Banach spaces. In this paper, we can see the complemented Banach subspaces of $wL\\sb{\\1}.$ In particular, the space $wL\\sb{\\1}$ contains complemented Banach sublattices that are isometrically isomorphic $l\\sp{p}\\ (1 \\le p < \\infty)$ and $c\\sb0.$ Moreover, if E is a separable reflexive Banach lattice, then the space $wL\\sb{\\1}$ contains a complemented sublattice that is isometrically isomorphic to E. Also we can see nonseparable complemented subspaces of $wL\\sb{\\1}.$ Finally, we show a couple of noncomplemented subspaces of $wL\\sb{\\1}.$","abstract_html":"The Banach envelope of $weakL\\sp1$ (denoted $wL\\sb{\\1})$ is a sort of universal Banach space for separable Banach spaces. In this paper, we can see the complemented Banach subspaces of $wL\\sb{\\1}.$ In particular, the space $wL\\sb{\\1}$ contains complemented Banach sublattices that are isometrically isomorphic <span class=\"etd-inline-math\">l\\sp{p} (1 \\le p &lt; \\infty)</span> and $c\\sb0.$ Moreover, if E is a separable reflexive Banach lattice, then the space $wL\\sb{\\1}$ contains a complemented sublattice that is isometrically isomorphic to E. Also we can see nonseparable complemented subspaces of $wL\\sb{\\1}.$ Finally, we show a couple of noncomplemented subspaces of $wL\\sb{\\1}.$","abstract_has_math":true,"creators":["Kang, Jeongheung"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Peck, Tenney"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T12:02:35Z","date_published":"2011-05-07T12:02:35Z","updated_at":"2026-07-22T22:25:12Z","subjects":["Mathematics"],"languages":["eng"],"rights":["Copyright 1995 Kang, Jeongheung"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9522128","(UMI)AAI9522128"],"render_values":[{"text":"AAI9522128","href":null,"code":true},{"text":"(UMI)AAI9522128","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/19279","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Peck, Tenney"]},{"key":"dc:creator","label":"Author","values":["Kang, Jeongheung"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:02:35Z","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 Kang, Jeongheung"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9522128","(UMI)AAI9522128","http://hdl.handle.net/2142/19279"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The Banach envelope of $weakL\\sp1$ (denoted $wL\\sb{\\1})$ is a sort of universal Banach space for separable Banach spaces. In this paper, we can see the complemented Banach subspaces of $wL\\sb{\\1}.$ In particular, the space $wL\\sb{\\1}$ contains complemented Banach sublattices that are isometrically isomorphic $l\\sp{p}\\ (1 \\le p < \\infty)$ and $c\\sb0.$ Moreover, if E is a separable reflexive Banach lattice, then the space $wL\\sb{\\1}$ contains a complemented sublattice that is isometrically isomorphic to E. Also we can see nonseparable complemented subspaces of $wL\\sb{\\1}.$ Finally, we show a couple of noncomplemented subspaces of $wL\\sb{\\1}.$","Made available in DSpace on 2011-05-07T12:02:35Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9522128.pdf: 2016745 bytes, checksum: 3c67bd32f27c077acb26c7ef1aa1e7f4 (MD5) Previous issue date: 1995","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:35:52Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:14:18-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Complemented subspaces of weakL(1)"]}]}],"canonical_facts":{"dc:contributor":["Peck, Tenney"],"dc:creator":["Kang, Jeongheung"],"dc:date":["2011-05-07T12:02:35Z","10000-01-01","1995"],"dc:description":["The Banach envelope of $weakL\\sp1$ (denoted $wL\\sb{\\1})$ is a sort of universal Banach space for separable Banach spaces. In this paper, we can see the complemented Banach subspaces of $wL\\sb{\\1}.$ In particular, the space $wL\\sb{\\1}$ contains complemented Banach sublattices that are isometrically isomorphic $l\\sp{p}\\ (1 \\le p < \\infty)$ and $c\\sb0.$ Moreover, if E is a separable reflexive Banach lattice, then the space $wL\\sb{\\1}$ contains a complemented sublattice that is isometrically isomorphic to E. Also we can see nonseparable complemented subspaces of $wL\\sb{\\1}.$ Finally, we show a couple of noncomplemented subspaces of $wL\\sb{\\1}.$","Made available in DSpace on 2011-05-07T12:02:35Z (GMT). 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