Isometric shifts on C0(X) ✩

For a linear isometry T :C0(X)→C0(Y ) of finite corank, there is a cofinite subset Y1 of Y such that Tf|Y1 = h·f ◦ϕ is a weighted composition operator and X is homeomorphic to a quotient space of Y1 modulo a finite subset. When X = Y, such a T is called an isometric quasi-n-shift on C0(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 .  2002 Elsevier Science (USA). All rights reserved.