Disjointness preserving shifts on C-0(X)

作者：Chen, Li Shu; Jeang, Jyh Shyang; Wong, Ngai Ching^*

来源：Journal of Mathematical Analysis and Applications, 2007, 325(1): 400-421.

DOI：10.1016/j.jmaa.2006.01.067

• shifts
• quasi-shifts
• disjointness preserving operators
• Fredholm composition operators

We study disjointness preserving (quasi-)n-shift operators on C-0(X), where X is locally compact and Hausdorff. When C-0(X) admits a quasi-n-shift T, there is a countable subset of X-infinity = X U {infinity} equipped with a tree-like structure, called phi-tree, with exactly n joints such that the action of T on C-0(X) can be implemented as a shift on the phi-tree. If T is an n-shift, then the phi-tree is dense in X and thus X is separable. By analyzing the structure of the phi-tree, we show that every (quasi-)n-shift on c(0) can always be written as a product of n (quasi-)1-shifts. Although it is not the case for general C-0(X) as shown by our counter examples, we can do so after dilation.

• 出版日期2007-1-1
• 单位中山大学