  We study in this paper the concept of bounded point evaluations for cyclic
operators. We give a negative answer to a question of L.R. Williams {\it
Dynamic Systems and Apllications} 3(1994) 103-112. Furthermore, we generalize
some results of Williams and give a simple proof of theorem 2.5 of L.R.
Williams (The Local Spectra of Pure Quasinormal Operators J. Math. anal. Appl.
187(1994) 842-850) that non normal hyponormal weighted shifts have fat local
spectra.
