Operators with $C^* $-algebra generated by a unilateral shift.
Conway, John B.; McGuire, Paul
If T is an operator on a Hilbert space H, this paper gives necessary and sufficient condition on T such that $C^*(T)$, the $C^*$-algebra generated by T, is generated by a unilateral shift of some multiplicity. This result is then specialized to the cases in which $T$ is a hyponormal or subnormal operator. In particular, it is shown how to prove a recent conjecture of C.R. Putnam as a consequence of our result.