On p-operator spaces and their applications

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2010

Author dc:creator

• Lee, Jung Jin

Contributors dc:contributor

• Ruan, Zhong-Jin
• Boca, Florin
• Junge, Marius
• Erdogan, M. Burak

• p-operator space
• pseudofunction algebra
• pseudomeasure algebra
• Figa-Talamanca-Herz algebra

Statement dc:rights

• Copyright 2010 Jung Jin Lee

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/16714

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/16714