遗传C＊-子代数与可补闭子模的关系定理

The Relation Theorem of Hereditary C~*-Subalgebras and Complemented Submodules

设E是Hilbert C*-模，证明了E的每个闭子模均可补的充要条件是K(E)的每个非零遗传C*-子代数B，均有形式B=pK(E)p，其中P为L(E)中投影元．

Let E be a Hilbert C~*-module. We prove that each closed submodule of E is a complemented submodule if and only if each non-zero hereditary C~*-subalgebra B of K(E) has the form B = pK(E)p, where p is a projection in L(E).