Fredholm Weighted Generalized Composition Operators

Abstract

In the present paper, properties of the self map on $$\mathbb {D}$$ , the open unit disc, and complex valued mapping on $$\mathbb {D}$$ are obtained when the induced k th-order weighted generalized composition operator on weighted Hardy space is Fredholm. We also describe the action of the adjoint of generalized multiplication, generalized composition and $$k{th}$$ -order weighted generalized composition operators on the derivative evaluation kernel functions, which in turn provide some invariant subspaces for these operators.