On the Banach–Stone problem
Tom 155 / 2003
Studia Mathematica 155 (2003), 95-105
MSC: 46B04, 46E40, 46E15.
DOI: 10.4064/sm155-2-1
Streszczenie
Let and Y be locally compact Hausdorff spaces, let E and F be Banach spaces, and let T be a linear isometry from C_0(X,E) into C_0(Y,F). We provide three new answers to the Banach–Stone problem: (1) T can always be written as a generalized weighted composition operator if and only if F is strictly convex; (2) if T is onto then T can be written as a weighted composition operator in a {weak} sense; and (3) if T is onto and F does not contain a copy of \ell _2^\infty then T can be written as a weighted composition operator in the classical sense.
