## Abstract

D. Blecher and V. Paulsen showed that the Haagerup tensor product V ⊗^{h} W for operator spaces V and W preserves inclusions. It is proved to also preserve complete quotient maps, and to be self-dual in the sense that it induces the Haagerup norm on the algebraic tensor product V^{*} ⊗ W^{*}. The full operator dual space (V ⊗^{h} W)^{*} is computed. It coincides with the natural operator space \ ̃gG_{2}(V, W^{*}) of maps θ{symbol}: V → W^{*} which have completely bounded factorizations through Hilbert spaces (with vectors identified with row matrices). More generally, one has the natural complete isometry \ ̃gG_{2}(V ⊗^{h} W, X) ≊ \ ̃gG_{2}(V, \ ̃gG_{2}(W, X)). Given Hilbert spaces H and K with vectors regarded as column matrices, it is shown that one may identify the operator spaces B(H, K) and CB(H, K).

Original language | English (US) |
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Pages (from-to) | 257-284 |

Number of pages | 28 |

Journal | Journal of Functional Analysis |

Volume | 100 |

Issue number | 2 |

DOIs | |

State | Published - Sep 1991 |

## ASJC Scopus subject areas

- Analysis