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
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10.1512/iumj.2004.53.2559
10.1512/iumj.2004.53.2559
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Indiana Univ. Math. J. 53 (2004) 1537 - 1550
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