Fractal Property in B(H) Induced by Partial Isometries

Abstract

We consider the groupoid C*-dynamical systems \({(A,{\mathbb G},\alpha ),}\) where A is a C*-algebra in \({B(H),{\mathbb G}}\) is a certain groupoid, and α is an embedding groupoid action of \({{\mathbb G},}\) acting on A in B(H). In particular, we are interested in the case where the groupoid \({{\mathbb G}}\) is a fractaloid, a groupoid with fractal property. Moreover, we restrict our interests to the case where \({{\mathbb G}}\) is generated by finitely many partial isometries in B(H). We observe the basic properties of such C*-dynamical systems.