论文标题
Banach晶格值连续函数的亚amir-cambern定理
An Amir-Cambern theorem for subspaces of Banach lattice-valued continuous functions
论文作者
论文摘要
对于$ i = 1,2 $，让$ e_i $成为$ \ m athbb {r} $的反射性班克晶格，带有特定参数$λ^+（e_i）> 1 $，让$ k_i $成为本地紧凑（hausdorff）拓扑空间，让$ \ \ \ \ \ mathcal { $ \ MATHCAL {C} _0（k_i，e_i）$，使得Choquet Boundare $ \ Mathcal {Ch} _ {\ Mathcal {\ Mathcal {h} _i} k_i $ of $ \ MATHCAL {我们表明，如果存在同构$ t \ colon \ Mathcal {h} _1 \ to \ Mathcal {h} _2 $ at $ \ vert t \ vert t \ vert \ cdot \ cdot \ vert \ vert \ vert t^{ - 1} $ t $和$ t^{ - 1} $保存阳性，然后$ \ Mathcal {ch} _ {\ Mathcal {h} _1} k_1 $是同型到$ \ Mathcal {ch} _ {
For $i=1,2$, let $E_i$ be a reflexive Banach lattice over $\mathbb{R}$ with a certain parameter $λ^+(E_i)>1$, 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 $\mathcal{Ch}_{\mathcal{H}_i} K_i$ of $\mathcal{H}_i$ is a weak peak point. We show that if there exists an isomorphism $T\colon \mathcal{H}_1 \to \mathcal{H}_2$ with $\Vert T \Vert \cdot \Vert T^{-1} \Vert<\min \lbrace λ^+(E_1), λ^+(E_2) \rbrace$ such that $T$ and $T^{-1}$ preserve positivity, then $\mathcal{Ch}_{\mathcal{H}_1} K_1$ is homeomorphic to $\mathcal{Ch}_{\mathcal{H}_2} K_2$.
