International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 30, Pages 1899-1909
doi:10.1155/S0161171203209042

On the largest analytic set for cyclic operators

Abstract

We describe the set of analytic bounded point evaluations for an arbitrary cyclic bounded linear operator T on a Hilbert space ℋ; some related consequences are discussed. Furthermore, we show that two densely similar cyclic Banach-space operators possessing Bishop's property (β) have equal approximate point spectra.