IUMJ

Title: Common cyclic vectors for normal operators

Authors: William T. Ross and Warren R. Wogen

Issue: Volume 53 (2004), Issue 6, 1537-1550

Abstract:

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.