LAUSR

We study some classical operators defined on the weighted Bergman Fréchet space Apα+ (resp. weighted Bergman (LB)-space Apα− ) arising as the projective limit (resp. inductive limit) of the standard weighted Bergman spaces into the growth Fréchet space H∞ α+ (resp. growth (LB)-space H∞ α− ), which is the projective limit (resp. inductive limit) of the growth Banach spaces. We show that, for an analytic self map φ of the unit disc D , the continuities of the weighted composition operator Wg,φ , the Volterra integral operator Tg , and the pointwise multiplication operator Mg 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 Wg,φ acting on a weighted Bergman Fréchet or (LB)-space. Some results concerning eigenvalues of such composition operators Cφ are presented.