算子空间的原子性

Nuclearity of Operator Spaces

研究了算子空间的原子性.证明了算子空间V是原子当且仅当V是正合且有限内射;V内的任意一个有限维算子子空间是原子当且仅当V是原子且V内任意有限维算子子空间是V的完全补。因此作为推论,得到了无限维算子空间V的任意有限维子空间是原子,则V是1-Hilbertian和1-齐次。

This paper studies the nuclearity for operator space V is nuclear if and only if V is operator spaces. The authors show that an exact and finitely injective, and also prove that every finite dimensional operator subspace in V is nuclear if and only if V is nuclear and every finite dimensional operator subspace in V is completely complement in V. As a corollary, it is obtained that if every finite dimensionM subspaee of an infinite dimensional operator space V is nuclear, then V is 1-Hilbertian and 1-homogeneous.