一个具有CBAP且无完全有界基的可分希尔伯特算子空间
A Separable Hilbertian Operator Space with CBAP and No Completely Bounded Basis
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中文总结 AI 辅助
本文构造了一个具有1-CBAP但无完全有界基的可分希尔伯特算子空间，表明完全有界框架不必产生完全有界基，并利用Oikhberg定理完成构造。
中文摘要 AI 辅助
Liu和Ruan证明了可分算子空间具有完全有界逼近性质当且仅当它承认一个完全有界框架。我们表明，即使对于希尔伯特算子空间，这样的框架也不必产生完全有界基。更精确地说，我们构造了一个具有$1$-CBAP但没有完全有界基的可分希尔伯特算子空间。我们的构造依赖于Oikhberg的一个定理，该定理提供了合适算子空间上完全有界映射的结构描述。
英文摘要
Liu and Ruan showed that a separable operator space has the completely bounded approximation property if and only if it admits a completely bounded frame. We show that, even for Hilbertian operator spaces, such a frame need not give rise to a completely bounded basis. More precisely, we construct a separable Hilbertian operator space with the $1$-CBAP but with no completely bounded basis. Our construction relies on a theorem of Oikhberg that provides a structural description of the completely bounded maps on a suitable operator space.
