我们证明了Banach空间$\mathrm{<trans\; data-src="X">X（X）</trans>}$对于每个可分Banach空间具有有界逼近性质的当且仅当$\mathrm{<trans\; data-src="Z">Z轴</trans>}$和每个内射算子$\mathrm{<trans\; data-src="T">吨</trans>}$从$\mathrm{<trans\; data-src="Z">Z轴</trans>}$到$\mathrm{<trans\; data-src="X">X（X）</trans>}$，存在一个网络$<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}}<trans\; data-src=")">)</trans>$有限秩算子的$\mathrm{<trans\; data-src="Z">Z轴</trans>}$到$\mathrm{<trans\; data-src="X">X（X）</trans>}$具有$<trans\; data-src="\Vert ">\Vert </trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}}<trans\; data-src="\Vert ">\Vert </trans><trans\; data-src="\le ">\le </trans>{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="T">吨</trans>}}$这样的话${<trans\; data-src="lim\hspace{0.17em}">林</trans>}_{\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}}<trans\; data-src="\Vert ">\Vert </trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}}\mathrm{<trans\; data-src="z">z（z）</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="T">吨</trans>}\mathrm{<trans\; data-src="z">z（z）</trans>}<trans\; data-src="\Vert ">\Vert </trans><trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="0">0</trans>}$对于每个$\mathrm{<trans\; data-src="z">z（z）</trans>}<trans\; data-src="\in ">\in </trans>\mathrm{<trans\; data-src="Z">Z轴</trans>}$.