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Embedding of C q and R q into noncommutative L p -spaces, 1≤p<q≤2

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We prove that a quotient of a subspace of C p ⊕ p R p (1≤p<2) embeds completely isomorphically into a noncommutative L p -space, where C p and R p are respectively the p-column and p-row Hilbertian operator spaces. We also represent C q and R q (p<q≤2) as quotients of subspaces of C p ⊕ p R p . Consequently, C q and R q embed completely isomorphically into a noncommutative L p (M). We further show that the underlying von Neumann algebra M cannot be semifinite.

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  1. Laboratoire de Mathématiques, Université de Franche-Comté, 25030, Besançon, cedex, France

    Quanhua Xu

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  1. Quanhua Xu
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Xu, Q. Embedding of C q and R q into noncommutative L p -spaces, 1≤p<q≤2. Math. Ann. 335, 109–131 (2006). https://doi.org/10.1007/s00208-005-0732-5

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  • DOI: https://doi.org/10.1007/s00208-005-0732-5

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