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On p-operator spaces and their applications

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Title: On p-operator spaces and their applications
Author(s): Lee, Jung Jin
Director of Research: Ruan, Zhong-Jin
Doctoral Committee Chair(s): Boca, Florin
Doctoral Committee Member(s): Ruan, Zhong-Jin; Junge, Marius; Erdogan, Burak
Department / Program: Mathematics
Discipline: Mathematics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): p-operator space pseudofunction algebra pseudomeasure algebra Figa-Talamanca-Herz algebra
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.
Issue Date: 2010-08-20
Rights Information: Copyright 2010 Jung Jin Lee
Date Available in IDEALS: 2010-08-20
Date Deposited: 2010-08

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