Analogs of Cuntz algebras on L^p spaces

2012/01/20 by N. Christopher Phillips, Phillips, N. Christopher · 3 citations
Mathematics · Medicine · #47L10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Ophthalmology and Eye Disorders #Primary 46H05 #Secondary 46H35 #math.FA #math.OA #msc:46H05 #msc:46H35 #msc:47L10

paper · pdf · doi:10.48550/arxiv.1201.4196

60 pages; AMSLaTeX

arxiv created 2012/01/20 · openalex publication_date 2012/01/20 · arxiv updated 2012/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For d = 2, 3, … and p ∈ [1, ∞), we define a class of representations ρ of the Leavitt algebra L_d on spaces of the form L^p (X, μ), which we call the spatial representations. We prove that for fixed d and p, the Banach algebra O_d^p obtained as the closure of the image of L_d under the representation ρ is the same for all spatial representations ρ. When p = 2, we recover the usual Cuntz algebra O_d. We give a number of equivalent conditions for a representation to be spatial. We show that for distinct p₁ and p₂ in [1, ∞) and arbitrary d₁ and d₂ in \ 2, 3, … \, there is no nonzero continuous homomorphism from O_d1^p₁ to O_d2^p₂.

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