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Representation of contractively complemented Hilbertian operator spaces on the Fock space


The operator spaces H nk, 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 H nk to a row or column space is explicitly calculated. ©2005 American Mathematical Society.

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