The Local Theory of Completely 1-Summing Mapping Spaces

In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions injectivity, reflexivity, exactness, nuclearity and finite-representability First obtain that if V has WEP, is locally reflexive (Ⅱ1(⋅,⋅), π1(⋅)) only it (Ⅰ(⋅,⋅), t(⋅)). Furthermore prove an operator space ⊆ B(H) exact finitely representable {Mn}n∈N π1(⋅)). At last, show = C.