Representation of contractively complemented Hilbertian operator spaces on the Fock space

Neal, Matthew; Russo, Bernard

doi:10.1090/S0002-9939-05-08130-X

Representation of contractively complemented Hilbertian operator spaces on the Fock space
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Proc. Amer. Math. Soc. 134 (2006), 475-485 Request permission

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 a row or column space is explicitly calculated.

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