Further properties of ℓ^p dimension

2012/02/23 by Antoine Gournay, Gournay, Antoine
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group Theory (math.GR) #math.FA #math.GR

paper · pdf · doi:10.48550/arxiv.1202.5266

22 pages

openalex publication_date 2012/02/23 · arxiv created 2012/03/23 · arxiv updated 2012/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article establishes more properties of the ℓ^p dimension introduced in a previous article. Given an amenable group Γ acting by translation on ℓ^p(Γ), this is just a number, associated to the (usually infinite dimensional) subspaces Y of ℓ^p(G) which are invariant under the action of G, satisfying dimension-like properties. As a consequence, for p∈ [1,2], if Y is a closed non-trivial Γ-invariant subspace of ℓ^p(Γ;V) and let Y_n is an increasing sequence of closed Γ-invariant subspace such that \srl∪ Y_n = ℓ^p(Γ;V), then there exist a k such that Y_k ∩ Y ≠ \0\.

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