On p-operator spaces and their applications

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

Lee, Jung Jin

关键词: p-operator space;    pseudofunction algebra;    pseudomeasure algebra;    Figa-Talamanca-Herz algebra;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/16714/Lee_JungJin.pdf?sequence=3&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

There have been a lot of research done on the relationship between locally compact groups and algebrasassociated 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.