Open AccessThe Cesàro operator on weighted Bergman Fréchet and (LB)-spaces of analytic functions
Author(s) -
Ersin Kızgut
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2112049k
Subject(s) - mathematics , schauder basis , bergman space , bounded function , space (punctuation) , order (exchange) , operator (biology) , pure mathematics , mathematical analysis , combinatorics , banach space , linguistics , philosophy , biochemistry , chemistry , finance , repressor , transcription factor , economics , gene
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 ?-.