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中文摘要：
讨论Banach空间中线性算子的连续的Moore-Penrose齐性广义逆的一个特征性质,即线性算子T存在连续的Moore-Penrose齐性广义逆Th的情况下,可在一定的条件下证得T为闭算子,且T的值域R（T）也是闭的.为证此性质,主要应用Moore-Penrose齐性广义逆的定义,及有界拟线性投影的拟线性.并证得T的定义域D（T）在一定条件下有代数直和分解,D（T）=^-N（T）C（T）.继而证得了T为闭算子.
英文摘要：
A property of continuous Moore - Penrose homogeneous generalized inverse of linear operator in Banach spaces is given. If linear operator T has continuous Moore - Penrose homogeneous generalized inverse T^h, it can be shown that T is closed operator, and R （T） is closed, under some conditions. In order to prove these properties, the definition of Moore - Penrose homogeneous generalized inverse and quasi -linear of boundary quasi -linear projector are used. Under some conditions, it is shown that D（T） has direct sum of algebras D（T） =^-N（T） C（T）. This implies that T is closed operator.
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