For a pure bounded rationally cyclic subnormal operator on a separable complex Hilbert space , Conway and Elias showed that . This article examines the property for rationally multicyclic (-cyclic) subnormal operators. We show that there exists a -cyclic irreducible subnormal operator with . We also show the following. For a pure rationally -cyclic subnormal operator on with the minimal normal extension on , let . Suppose that is pure. Then .
"Spectral picture for rationally multicyclic subnormal operators." Banach J. Math. Anal. 13 (1) 151 - 173, January 2019. https://doi.org/10.1215/17358787-2018-0020