On p-approximation properties for p-operator spaces

Guimei An, Jung Jin Lee, Zhong Jin Ruan

Research output: Contribution to journalArticlepeer-review


This paper has a two-fold purpose. Let 1<p<∞ We first introduce the p-operator space injective tensor product and study various properties related to this tensor product, including the p-operator space approximation property, for p-operator spaces on Lp-spaces. We then apply these properties to the study of the pseudofunction algebra PFp(G), the pseudomeasure algebra PMp(G), and the Figà-Talamanca-Herz algebra Ap(G) of a locally compact group G. We show that if G is a discrete group, then most of approximation properties for the reduced group C*-algebra Cλ*(G), the group von Neumann algebra VN(G), and the Fourier algebra A(G) (related to amenability, weak amenability, and approximation property of G) have the natural p-analogues for PFp(G), PMp(G), and Ap(G), respectively. The p-completely bounded multiplier algebra McbAp(G) plays an important role in this work.

Original languageEnglish (US)
Pages (from-to)933-974
Number of pages42
JournalJournal of Functional Analysis
Issue number4
StatePublished - Aug 2010


  • Figà-Talamanca-Herz algebras
  • P-Approximation property
  • P-Completely bounded multipliers
  • P-Operator spaces
  • P-Pseudofunction algebras

ASJC Scopus subject areas

  • Analysis


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