International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 30, Pages 1899-1909

On the largest analytic set for cyclic operators

A. Bourhim

The Abdus Salam International Centre for Theoretical Physics, Mathematics Section, Strada Costiera 11, Trieste 34100, Italy

Received 15 September 2002

Copyright © 2003 A. Bourhim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We describe the set of analytic bounded point evaluations for an arbitrary cyclic bounded linear operator T on a Hilbert space ; 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.