关于内积空间中正交补集的一个注记

A Note on the Orthogonal Complementary Set in Inner Product Space

指出文〔1〕中一个命题的错误,构造反例说明对于一般的内积空间及其子集M,(M~⊥)~⊥不一定是包含M的最小闭子空间。同时给出此命题成立的充要条件及相关结果。

A Counterexample is constructed in this paper to point out a mistake in [1], that is ,for an inner product space H and its subset M,(M⊥)⊥ is generally not the smallest closed subspace of H which contains M. We give a sufficient and necessary condition for this relation to be available. Other relating topics are discussed as well.