Geodesic
The Cesàro operator on weighted Bergman Fréchet and (lb)-spaces of analytic functions
Filomat, Tome 35 (2021) no. 12, p. 4049

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DOI

The spectrum of the Cesàro operator C is determined on the spaces which arises as intersections A p α+ (resp. unions A p α−) of Bergman spaces A p α of order 1 p ∞ induced by standard radial weights (1 − |z|) α , for 0 α ∞. We treat them as reduced projective limits (resp. inductive limits) of weighted Bergman spaces A p α , with respect to α. 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 Fréchet-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 A p α+ and A p α− .
DOI : 10.2298/FIL2112049K
Classification : 47A10, 47B38, 46A11, 46A13, 46E10, 47B10
Keywords: Cesàro operator, weighted spaces of analytic functions, Bergman spaces, Fréchet spaces, (LB)-spaces, spectrum 
Ersin Kızgut. The Cesàro operator on weighted Bergman Fréchet and (lb)-spaces of analytic functions. Filomat, Tome 35 (2021) no. 12, p. 4049 . doi: 10.2298/FIL2112049K
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     author = {Ersin K{\i}zgut},
     title = {The {Ces\`aro} operator on weighted {Bergman} {Fr\'echet} and (lb)-spaces of analytic functions},
     journal = {Filomat},
     pages = {4049 },
     year = {2021},
     volume = {35},
     number = {12},
     doi = {10.2298/FIL2112049K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2112049K/}
}
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