Isometric shifts on [formula omitted

Abstract

For a linear isometry T :C 0(X)→C 0(Y) of finite corank, there is a cofinite subset Y 1 of Y such that Tf |Y 1 =h·f∘ϕ is a weighted composition operator and X is homeomorphic to a quotient space of Y 1 modulo a finite subset. When X=Y, such a T is called an isometric quasi- n-shift on C 0(X) . In this case, the action of T can be implemented as a shift on a tree-like structure, called a T-tree, in M(X) with exactly n joints. The T-tree is total in M(X) when T is a shift. With these tools, we can analyze the structure of T.