Self-duality for the Haagerup tensor product and Hilbert space factorizations
Self-duality for the Haagerup tensor product and Hilbert space factorizations
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Haagerup 张量积和希尔伯特空间分解的自对偶性
DOI：
10.1016/0022-1236(91)90111-h
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发表时间：
1991
影响因子：
1.7
通讯作者：
Z. Ruan
中科院分区：
文献类型：
--
作者：
E. Effros;Z. Ruan
摘要D. Blecher和V. Paulsen证明了算子空间V和W的Haagerup张量积V h W保持包含。证明了它也保持完全商映射，并且是自对偶的，因为它在代数张量积V W上导出了Haagerup范数。计算了全算子对偶空间（V <$h W）的空间维数.它与自然算子空间\n gG 2（V，W <$）相一致，该自然算子空间是映射<$：V→ W <$的空间，该空间具有通过希尔伯特空间的完全有界分解（其中向量与行矩阵相同）。更一般地说，有自然的完全等距\gG 2（V h W，X）\gG 2（V，\gG 2（W，X））。给定Hilbert空间H和K，其向量为列矩阵，证明了算子空间B（H，K）和CB（H，K）是相同的.
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: 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).