C^＊代数上部分矩阵的投影补

The Projective Completions of Partial Matrices over a C^＊ -Algebra

在有单位元的C*-代数上引入投影矩阵的概念,讨论了其性质,证明了C*-代数上二阶矩阵成为投影矩阵的充分必要条件.在此基础上,研究了C*-代数上部分矩阵的投影补问题,得到两类二阶部分矩阵有投影补的充分必要条件.

The concept of projective matix over an unital C^＊-algebra was introduced and its property discussed. A sufficient and necessary condition to determine a 2-order matrix over a unital C^＊ -algebra was proved. On this base, the projective completions problem for two partial matrices was studied ,and sufficient and necessary conditions for two partial matrices having projective completions were obtained.