International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 30, Pages 1899-1909
On the largest analytic set for cyclic operators
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 on a Hilbert space
; some related consequences are discussed. Furthermore, we
show that two densely similar cyclic Banach-space operators
possessing Bishop's property have equal approximate point spectra.