Quasi-Locality and Property A

2018/09/03 by Ján Špakula, Jiawen Zhang, Špakula, Ján +1 · 3 citations
Mathematics · #20F65 #46H35 #46J40 #47L10 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1809.00532

openalex publication_date 2018/09/03 · openalex created_date 2018/09/27 · openalex updated_date 2026/07/28

Abstract

Let X be a metric space with bounded geometry, p∈\0\ ∪ [1,∞], and let E be a Banach space. The main result of this paper is that either if X has Yu's Property A and p∈(1,∞), or without any condition on X when p∈\0,1,∞\, then quasi-local operators on ℓ^p(X,E) belong to (the appropriate variant of) Roe algebra of X. This generalises the existing results of this type by Lange and Rabinovich, Engel, Tikuisis and the first author, and Li, Wang and the second author. As consequences, we obtain that uniform ℓ^p-Roe algebras (of spaces with Property A) are closed under taking inverses, and another condition characterising Property A, akin to operator norm localisation for quasi-local operators.

Citations

• Crossed products of L^p operator algebras and the K-theory of Cuntz algebras on L^p spaces

Cited by

• A note on the quasi-local algebra of expander graphs
• Asymptotic expansion for groupoids and Roe type algebras
• Structure and K-theory of ℓ^p uniform Roe algebras

Related

• Quasi-local Algebras and Asymptotic Expanders
• A Gelfand-type duality for coarse metric spaces with property A
• Uniform Local Amenability
• The principle of local reflexivity and an extension of the identity\n mathcal B(E,X^**)\≅ mathcal B(E,X)^**
• Morita equivalence of two ℓ^p Roe-type algebras