On compact transformation semigroups with discrete spectrum. (English) Zbl 0586.22002
Let (G,X) be a compact transformation semigroup. Suppose that (G,X) is topologically transitive, i.e. Gx is dense in X for some \(x\in X\). A function f in C(X) is called an eigenfunction if there is a function \(\lambda\) on G such that \(f(gx)=\lambda (g) f(x)\) for all \(g\in G\), \(x\in X\). If the closed linear span of the set of eigenfunctions is C(X) then (G,X) is said to have a topological discrete spectrum.
The aim of this paper is to obtain characterizations of such transformation semigroups with topological discrete spectra.
The aim of this paper is to obtain characterizations of such transformation semigroups with topological discrete spectra.
Reviewer: J.W.Baker
MSC:
22A15 | Structure of topological semigroups |
54H15 | Transformation groups and semigroups (topological aspects) |
22A25 | Representations of general topological groups and semigroups |