| Volume 1, Number 2, 2011, Pages 279-290 DOI：10.11948/2011019 |
| Duality theory of regularized resolvent operator family |
| Jizhou Zhang,Yeping Li |
| Keywords:k-regularized resolvent operator family, pseudo k-resolvent, duality, Favard space. |
| Abstract: |
| Let \( k \in C(R^+)\), A be a closed linear densely defined operator in the Banach space \(X\) and \( \{R(t)\}_{t\geq 0} \) be an exponentially bounded \(k\)-regularized resolvent operator families generated by A. In this paper, we mainly study pseudo k-resolvent and duality theory of k-regularized resolvent operator families. The conditions that pseudo k-resolvent become k-resolvent of the closed linear densely defined operator A are given. The some relations between the duality of the regularized resolvent operator families and the generator A are gotten. In addition, the corresponding results of duality of \(k\)-regularized resolvent operator families in Favard space are educed. |
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