C-Subalgebras Generated by a Single Operator in B(H)

摘要

In this paper, we characterize a C-subalgebra C(x) of B(H), generated by a single operator x.We show that if x is polar-decomposed by aq, where a is the partial isometry part and q is the positive operator part of x, then C(x) is -isomorphic to the groupoid crossed product algebra Aq ×αGa, where Aq = C (q) and Ga is the graph groupoid induced by a partial isometry part a of x.