Abstract
We deal with isomorphic Banach-Stone type theorems for closedsubspaces of vectorvaluedcontinuous functions. Let F= R or C.
For i= 1 , 2 ,let Ei be a reflexive Banach space over F with a certain parameter λ(Ei) > 1 ,which in the real case coincides with the Schaffer constant of Ei, let Ki be alocally compact (Hausdorff) topological space and let Hi be a closed subspaceof C(Ki, Ei) such that each point of the Choquet boundary ChHiKi of Hi is aweak peak point. We show that if there exists an isomorphism T: H1RIGHTWARDS ARROW H2 with| | T| | . | | T- 1| | < min { λ(E1) , λ(E2) } , then ChH1K1 is homeomorphic to ChH2K2.Next we provide an analogous version of the weak vectorvaluedBanach-Stonetheorem for subspaces, where the target spaces do not contain an isomorphic copyof c.