1997/09/26 by Francesco Fidaleo, Fidaleo, Francesco · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #funct-an #math.OA
paper · pdf · doi:10.48550/arxiv.funct-an/9709005
23 pages, LaTex
arxiv created 1997/09/26 · openalex publication_date 1997/09/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterize classes of linear maps between operator spaces E, F which factorize through maps arising in a natural manner via the Pisier vector-valued non-commutative Lp spaces Sp[E^*] based on the Schatten classes on the separable Hilbert space l2. These classes of maps can be viewed as quasi-normed operator ideals in the category of operator spaces, that is in non-commutative (quantized) functional analysis. The case p=2 provides a Banach operator ideal and allows us to characterize the split property for inclusions of W^*-algebras by the 2-factorable maps. The various characterizations of the split property have interesting applications in Quantum Field Theory.