For \(i=1,2\), let \(E_i\) be a reflexive Banach lattice over \({\mathbb {R}}\) with a certain parameter \(\lambda ^+(E_i)>1\), let \(K_i\) be a locally compact (Hausdorff) topological space and let \({\mathcal {H}}_i\) be a closed subspace of \({\mathcal {C}}_0(K_i, E_i)\) such that each point of the Choquet boundary \({\text {Ch}}_{{\mathcal {H}}_i} K_i\) of \({\mathcal {H}}_i\) is a weak peak point. We show that if there exists an isomorphism \(T:{\mathcal {H}}_1\rightarrow {\mathcal {H}}_2\) with \(\left\| T\right\| \cdot \left\| T^{-1}\right\| <\min \lbrace \lambda ^+(E_1), \lambda ^+(E_2) \rbrace\) such that T and \(T^{-1}\) preserve positivity, then \({\text {Ch}}_{{\mathcal {H}}_1} K_1\) is homeomorphic to \({\text {Ch}}_{{\mathcal {H}}_2} K_2\).

对于\（i = 1,2 \），令\（E_i \）是\（{\ mathbb {R}} \）上具有特定参数\（\ lambda ^ +（E_i）> 1 \ ），令\（K_i \）为局部紧凑（Hausdorff）拓扑空间，令\（{\ mathcal {H}} _ i \）为\（{\ mathcal {C}} _​​ 0（K_i，E_i ）\），这样\（{\ mathcal {H}} _ i \）的Choquet边界\（{\ text {Ch}} _ {{\ mathcal {H}} _ i} K_i \）的每个点都是弱的高峰点。我们证明如果存在同构\（T：{\ mathcal {H}} _ 1 \ rightarrow {\ mathcal {H}} _ 2 \）与\（\ left \ | T \ right \ | \ cdot \ left \ | T ^ {-1} \ right \ | <\ min \ lbrace \ lambda ^ +（E_1），\ lambda ^ +（E_2）\ rbrace \ ），使得T和\（T ^ {-1} \）保持正数，则\（{\ text {Ch}} _ {{\ mathcal {H}} _ 1} K_1 \）对\（{\ text {Ch}} _ {{\ mathcal {H}} _ 2} K_2 \）。