Title: DUALITY THEORY OF REGULARIZED RESOLVENT OPERATOR FAMILY
Abstract: Let <i>k</i> ∈ <i>C</i>(R<sup>+</sup>), <i>A</i> be a closed linear densely defined operator in the Banach space <i>X</i> and {<i>R</i>(<i>t</i>)}<sub><i>t</i></sub> ≥ 0 be an exponentially bounded <i>k</i>-regularized resolvent operator families generated by <i>A</i>. In this paper, we mainly study pseudo <i>k</i>-resolvent and duality theory of <i>k</i>-regularized resolvent operator families. The conditions that pseudo k-resolvent become <i>k</i>-resolvent of the closed linear densely defined operator <i>A</i> are given. The some relations between the duality of the regularized resolvent operator families and the generator <i>A</i> are gotten. In addition, the corresponding results of duality of <i>k</i>-regularized resolvent operator families in Favard space are educed.