Abstract
The spectrum of the Ces?ro operator C is determined on the spaces which arises as intersections Ap ?+ (resp. unions Ap ?-) of Bergman spaces Ap? of order 1 < p < 1 induced by standard radial weights (1-|z|)?, for 0 < ? < 1. We treat them as reduced projective limits (resp. inductive limits) of weighted Bergman spaces Ap?, with respect to ?. Proving that these spaces admit the monomials as a Schauder basis paves the way for using Grothendieck-Pietsch criterion to deduce that we end up with a non-nuclear Fr?chet-Schwartz space (resp. a non-nuclear (DFS)-space). We show that C is always continuous, while it fails to be compact or to have bounded inverse on Ap ?+ and Ap ?-.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
