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Representation of contractively complemented Hilbertian operator spaces and the Fock space

Matthew Neal·Bernard Russo
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Abstract

The operator spaces $H_n^k$ $1\le k\le n$, 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 $H_n^k$ to row or column space is explicitly calculated.

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Matthew Neal, Bernard Russo. 2004-10-14. Representation of contractively complemented Hilbertian operator spaces and the Fock space. https://arxiv.org/abs/math/0410337

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