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oai:www.ideals.illinois.edu:2142/16714 2023-07-10 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Ruan, Zhong-Jin Boca, Florin Ruan, Zhong-Jin Junge, Marius Erdogan, M. Burak Lee, Jung Jin 2010-08-20T17:55:43Z 2010-08-20T17:55:43Z 2010-08-20T17:55:43Z 2010-08 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 Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-07-09T13:11:37Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: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) http://hdl.handle.net/2142/16714 en Copyright 2010 Jung Jin Lee p-operator space pseudofunction algebra pseudomeasure algebra Figa-Talamanca-Herz algebra On p-operator spaces and their applications Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD