Affiliation:
1. Department of Mathematics, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia
Abstract
We consider an operator {S(t)}t≥0 on a Banach space X with generator A, characterized by being an α-times-integrated C-regularized semigroup. The adjoint family S*(t):X*→X* is introduced for analysis. {S*(t)}t≥0 maintains the characteristics of an α-times-integrated C-regularized semigroup, though with strong continuity and Bochner integrals being substituted by weak* continuity and weak* integrals, respectively. Our investigation focuses on the closed subspace X⊙, where {S*(t)}t≥0 exhibits strong continuity. Additionally, a comparison between the adjoint A* of A and the generator of the adjoint family is conducted.
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