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The Adjoint of α -Times-Integrated C -Regularized Semigroups

Author

Listed:
  • Mostafa Bachar

    (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.

Suggested Citation

  • Mostafa Bachar, 2024. "The Adjoint of α -Times-Integrated C -Regularized Semigroups," Mathematics, MDPI, vol. 12(10), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1561-:d:1396262
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