Turkish Journal of Mathematics
DOI
10.3906/mat-2101-95
Abstract
We study some classical operators defined on the weighted Bergman Frechet space $A^p_{\alpha+}$ (resp. weighted Bergman (LB)-space $A^p_{\alpha-}$) arising as the projective limit (resp. inductive limit) of the standard weighted Bergman spaces into the growth Frechet space $H^\infty_{\alpha+}$ (resp. growth (LB)-space $H^\infty_{\alpha-}$), which is the projective limit (resp. inductive limit) of the growth Banach spaces. We show that, for an analytic self map $\varphi$ of the unit disc $\mathbb{D}$, the continuities of the weighted composition operator $W_{g,\varphi}$, the Volterra integral operator $T_g$, and the pointwise multiplication operator $M_g$ defined via the identical symbol function are characterized by the same condition determined by the symbol's state of belonging to a Bloch-type space. These results have consequences related to the invertibility of $W_{g,\varphi}$ acting on a weighted Bergman Frechet or (LB)-space. Some results concerning eigenvalues of such composition operators $C_\varphi$ are presented.
Keywords
Weighted composition operator, Volterra operator, multiplication operator, Frechet spaces, (LB)-spaces, weighted spaces of analytic functions
First Page
1015
Last Page
1029
Recommended Citation
KIZGUT, ERSİN
(2021)
"Operators between different weighted Frechet and (LB)-spaces of analytic functions,"
Turkish Journal of Mathematics: Vol. 45:
No.
2, Article 28.
https://doi.org/10.3906/mat-2101-95
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss2/28
