Coarse geometry of operator spaces and complete isomorphic embeddings into ℓ₁ and c₀-sums of operator spaces

2022/11/21 by Braga, Bruno de Mendonça, Oikhberg, Timur
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2211.11854

Abstract

The nonlinear geometry of operator spaces has recently started to be investigated. Many notions of nonlinear embeddability have been introduced so far, but, as noticed before by other authors, it was not clear whether they could be considered ``correct notions''. The main goal of these notes is to provide the missing evidence to support that almost complete coarse embeddability is ``a correct notion''. This is done by proving results about the complete isomorphic theory of ℓ₁-sums of certain operators spaces. Several results on the complete isomorphic theory of c₀-sums of operator spaces are also obtained.

Related

• Towards a theory of coarse geometry of operator spaces
• Completely coarse maps are \mathbb R-linear
• On the small scale nonlinear theory of operator spaces
• On weaker notions of nonlinear embeddings between Banach spaces
• Lipschitz geometry of operator spaces and Lipschitz-free operator spaces