Classification of contractively complemented Hilbertian operator spaces
نویسندگان
چکیده
منابع مشابه
Classification of Contractively Complemented Hilbertian Operator Spaces
We construct some separable infinite dimensional homogeneous Hilbertian operator spaces H ∞ and H m,L ∞ , which generalize the row and column spaces R and C (the case m = 0). We show that separable infinitedimensional Hilbertian JC∗-triples are completely isometric to an element of the set of (infinite) intersections of these spaces . This set includes the operator spaces R, C, R ∩ C, and the s...
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The operator spaces Hk n 1 ≤ k ≤ n, generalizing the row and column Hilbert spaces, and arising in the authors’ previous study of contractively complemented subspaces of C∗-algebras, are shown to be homogeneous and completely isometric to a space of creation operators on a subspace of the anti-symmetric Fock space. The completely bounded Banach-Mazur distance from Hk n to row or column space is...
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In 1965, Ron Douglas proved that if X is a closed subspace of an L-space and X is isometric to another L-space, then X is the range of a contractive projection on the containing L-space. In 1977 Arazy-Friedman showed that if a subspace X of C1 is isometric to another C1-space (possibly finite dimensional), then there is a contractive projection of C1 onto X. In 1993 Kirchberg proved that if a s...
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Following Grothendieck’s characterization of Hilbert spaces we consider operator spaces F such that both F and F ∗ completely embed into the dual of a C*-algebra. Due to Haagerup/Musat’s improved version of Pisier/Shlyakhtenko’s Grothendieck inequality for operator spaces, these spaces are quotients of subspaces of the direct sum C ⊕ R of the column and row spaces (the corresponding class being...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2006
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2006.01.008