AI 中文总结
本文研究强面部对称空间的完备化与稠密子空间的性质，引入面稠密条件保证其完备化后仍为强面部对称空间，证明中性SFS-空间的不变稠密子空间可继承其结构，并给出相关例子与反例。
AI 中文摘要
我们研究强面部对称空间（SFS-空间）在完备化及过渡到范数稠密子空间时的性质。引入自然的面稠密条件，保证赋范SFS-空间的完备化仍为强面部对称空间。证明：当中性强面部对称空间的范数稠密子空间在环境广义Peirce投影下不变时，该子空间继承中性SFS-结构。给出若干例子与反例，包括迹类的中间子空间及$C[0,1]/subset L_1[0,1]$的稠密子空间。
英文摘要
We study the behavior of strongly facially symmetric spaces under completion and passage to norm-dense subspaces. We introduce a natural face-density condition guaranteeing that the completion of a normed SFS-space remains strongly facially symmetric. We prove that a norm-dense subspace of a neutral strongly facially symmetric space inherits the neutral SFS-structure whenever it is invariant under the ambient generalized Peirce projections. Several examples and counterexamples are presented, including intermediate subspaces of the trace class and the dense subspace $C[0,1]\subset L_1[0,1]$.
