Common cyclic vectors for normal operators William RossW. Wogen 47B15normal operatorscyclic vectors If $\mu$ is a finite compactly supported measure on $\mathbb{C}$, then the set $S_{\mu}$ of multiplication operators $M_{\phi} : L^{2}(\mu) \to L^{2}(\mu)$, $M_{\phi}f = \phi f$, where $\phi \in L^{\infty}(\mu)$ is injective on a set of full $\mu$ measure, is the complete set of cyclic multiplication operators on $L^{2}(\mu)$. In this paper, we explore the question as to whether or not $S_{\mu}$ has a common cyclic vector. Indiana University Mathematics Journal 2004 text pdf 10.1512/iumj.2004.53.2559 10.1512/iumj.2004.53.2559 en Indiana Univ. Math. J. 53 (2004) 1537 - 1550 state-of-the-art mathematics http://iumj.org/access/