Equations of the first kind and the inversion of series of resolvents of a closed operator

Abstract

Let $A$ be a densely defined closed operator in a complex Banach space $X.$ Conditions for left invertibility of operators of the form ${\sum }_{j=1}^{\infty }{a}_j({\alpha }_j-A{)}^{-1}$ are given. Several examples are considered.

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