{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/16714"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/16714","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On p-operator spaces and their applications","abstract":"There have been a lot of research done on the relationship between locally compact groups and algebras associated with them. For example, Johnson proved that a locally compact group G is amenable if and only if the convolution algebra L1(G) is amenable as a Banach algebra, and Ruan showed that G is amenable if and only if the Fourier algebra A(G) of G is operator amenable. Motivated by Ruan's work, we want to study G through tools from p-operator spaces. We _rst introduce the p-operator space and various p-operator space tensor products. We then study p-operator space approximation property and p-operator space completely bounded approximation property which are related to p-operator space injective tensor product. We then apply these properties to the study of the pseudofunction algebra PFp(G), the pseudomeasure algebra PMp(G), and the Fig_a-Talamanca-Herz Algebra Ap(G). Especially we show that if G is discrete, the most of approximation properties for the reduced group C_-algebra C_ _(G), the group von Neumann algebra V N(G), and the Fourier algebra A(G) (related to amenability, weak amenability, and approximation property of G) have natural p-analogues for PFp(G), PMp(G), and Ap(G). With help of Herz's work, we also study the stability of these properties. Finally we discuss the properties Cp, C0p , and C00p which are natural p-analogues of properties C, C0, and C00.","abstract_html":"There have been a lot of research done on the relationship between locally compact groups and algebras associated with them. For example, Johnson proved that a locally compact group G is amenable if and only if the convolution algebra L1(G) is amenable as a Banach algebra, and Ruan showed that G is amenable if and only if the Fourier algebra A(G) of G is operator amenable. Motivated by Ruan's work, we want to study G through tools from p-operator spaces. We _rst introduce the p-operator space and various p-operator space tensor products. We then study p-operator space approximation property and p-operator space completely bounded approximation property which are related to p-operator space injective tensor product. We then apply these properties to the study of the pseudofunction algebra PFp(G), the pseudomeasure algebra PMp(G), and the Fig_a-Talamanca-Herz Algebra Ap(G). Especially we show that if G is discrete, the most of approximation properties for the reduced group C_-algebra C_ _(G), the group von Neumann algebra V N(G), and the Fourier algebra A(G) (related to amenability, weak amenability, and approximation property of G) have natural p-analogues for PFp(G), PMp(G), and Ap(G). With help of Herz's work, we also study the stability of these properties. Finally we discuss the properties Cp, C0p , and C00p which are natural p-analogues of properties C, C0, and C00.","abstract_has_math":false,"creators":["Lee, Jung Jin"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Ruan, Zhong-Jin","Boca, Florin","Junge, Marius","Erdogan, M. Burak"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-08-20T17:55:43Z","date_published":"2010-08-20T17:55:43Z","updated_at":"2026-07-22T22:25:09Z","subjects":["p-operator space","pseudofunction algebra","pseudomeasure algebra","Figa-Talamanca-Herz algebra"],"languages":["en"],"rights":["Copyright 2010 Jung Jin Lee"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/16714","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ruan, Zhong-Jin","Boca, Florin","Junge, Marius","Erdogan, M. 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For example, Johnson proved that a locally compact group G is amenable if and only if the convolution algebra L1(G) is amenable as a Banach algebra, and Ruan showed that G is amenable if and only if the Fourier algebra A(G) of G is operator amenable. Motivated by Ruan's work, we want to study G through tools from p-operator spaces. We _rst introduce the p-operator space and various p-operator space tensor products. We then study p-operator space approximation property and p-operator space completely bounded approximation property which are related to p-operator space injective tensor product. We then apply these properties to the study of the pseudofunction algebra PFp(G), the pseudomeasure algebra PMp(G), and the Fig_a-Talamanca-Herz Algebra Ap(G). Especially we show that if G is discrete, the most of approximation properties for the reduced group C_-algebra C_ _(G), the group von Neumann algebra V N(G), and the Fourier algebra A(G) (related to amenability, weak amenability, and approximation property of G) have natural p-analogues for PFp(G), PMp(G), and Ap(G). With help of Herz's work, we also study the stability of these properties. Finally we discuss the properties Cp, C0p , and C00p which are natural p-analogues of properties C, C0, and C00.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-07-09T13:11:37Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 Lee_Jung Jin.tex: 275916 bytes, checksum: eab5ea7fa048e3c13b90f8d02e7d5645 (MD5) Lee_Jung Jin.pdf: 667833 bytes, checksum: 7b4e81a61cacfaf19a125592ca550cfe (MD5)","Made available in DSpace on 2010-08-20T17:55:43Z (GMT). No. of bitstreams: 4 Lee_Jung Jin.pdf: 667833 bytes, checksum: 7b4e81a61cacfaf19a125592ca550cfe (MD5) Lee_Jung Jin.tex: 275916 bytes, checksum: eab5ea7fa048e3c13b90f8d02e7d5645 (MD5) Lee_JungJin.pdf: 667833 bytes, checksum: 7b4e81a61cacfaf19a125592ca550cfe (MD5) license.txt: 4058 bytes, checksum: d6d3c5de7274a9fdc7614726b39453e7 (MD5)"]},{"key":"dc:title","label":"Title","values":["On p-operator spaces and their applications"]}]}],"canonical_facts":{"dc:contributor":["Ruan, Zhong-Jin","Boca, Florin","Junge, Marius","Erdogan, M. Burak"],"dc:creator":["Lee, Jung Jin"],"dc:date":["2010-08-20T17:55:43Z","2010-08"],"dc:description":["There have been a lot of research done on the relationship between locally compact groups and algebras associated with them. For example, Johnson proved that a locally compact group G is amenable if and only if the convolution algebra L1(G) is amenable as a Banach algebra, and Ruan showed that G is amenable if and only if the Fourier algebra A(G) of G is operator amenable. Motivated by Ruan's work, we want to study G through tools from p-operator spaces. We _rst introduce the p-operator space and various p-operator space tensor products. We then study p-operator space approximation property and p-operator space completely bounded approximation property which are related to p-operator space injective tensor product. We then apply these properties to the study of the pseudofunction algebra PFp(G), the pseudomeasure algebra PMp(G), and the Fig_a-Talamanca-Herz Algebra Ap(G). Especially we show that if G is discrete, the most of approximation properties for the reduced group C_-algebra C_ _(G), the group von Neumann algebra V N(G), and the Fourier algebra A(G) (related to amenability, weak amenability, and approximation property of G) have natural p-analogues for PFp(G), PMp(G), and Ap(G). With help of Herz's work, we also study the stability of these properties. Finally we discuss the properties Cp, C0p , and C00p which are natural p-analogues of properties C, C0, and C00.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-07-09T13:11:37Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 Lee_Jung Jin.tex: 275916 bytes, checksum: eab5ea7fa048e3c13b90f8d02e7d5645 (MD5) Lee_Jung Jin.pdf: 667833 bytes, checksum: 7b4e81a61cacfaf19a125592ca550cfe (MD5)","Made available in DSpace on 2010-08-20T17:55:43Z (GMT). No. of bitstreams: 4 Lee_Jung Jin.pdf: 667833 bytes, checksum: 7b4e81a61cacfaf19a125592ca550cfe (MD5) Lee_Jung Jin.tex: 275916 bytes, checksum: eab5ea7fa048e3c13b90f8d02e7d5645 (MD5) Lee_JungJin.pdf: 667833 bytes, checksum: 7b4e81a61cacfaf19a125592ca550cfe (MD5) license.txt: 4058 bytes, checksum: d6d3c5de7274a9fdc7614726b39453e7 (MD5)"],"dc:identifier":["http://hdl.handle.net/2142/16714"],"dc:language":["en"],"dc:rights":["Copyright 2010 Jung Jin Lee"],"dc:subject":["p-operator space","pseudofunction algebra","pseudomeasure algebra","Figa-Talamanca-Herz algebra"],"dc:title":["On p-operator spaces and their applications"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:09Z"}