Representation of contractively complemented Hilbertian operator spaces and the Fock space

Details Representation of contractively complemented Hilbertian operator spaces and the Fock space Representation of contractively complemented Hilbertian operator spaces and the Fock space

2004-10-14

arxiv.org/abs/math/0410337v1

Mathematics

Operator Algebras

11 pages

Scientific paper

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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