1991/09/01 by Edward G. Effros, Zhong‐Jin Ruan · 132 citations
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #Approximation property #Banach space #Bounded operator #Compact operator #Computer science #Extension (predicate logic) #Finite-rank operator #Mathematics #Nuclear operator #Operator (biology) #Operator space #Pseudo-monotone operator #Pure mathematics #Quasinormal operator #Space (punctuation) #Strictly singular operator #Tensor product
paper · pdf · doi:10.4153/cmb-1991-053-x
published in Canadian Mathematical Bulletin 34(3), 329-337 (Cambridge University Press)
openalex publication_date 1991/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Abstract The authors previously observed that the space of completely bounded maps between two operator spaces can be realized as an operator space. In particular, with the appropriate matricial norms the dual of an operator space V is completely isometric to a linear space of operators. This approach to duality enables one to formulate new analogues of Banach space concepts and results. In particular, there is an operator space version ⊗ μ of the Banach space projective tensor product , which satisfies the expected functorial properties. As is the case for Banach spaces, given an operator space V , the functor W |—> V ⊗ μ W preserves inclusions if and only if is an injective operator space.