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Adjoint bi-continuous semigroups and semigroups on the space of measures

Bálint Farkas (2011)

Czechoslovak Mathematical Journal

For a given bi-continuous semigroup ${(T (t))}_{t \geq 0}$ on a Banach space $X$ we define its adjoint on an appropriate closed subspace $X^{\circ}$ of the norm dual $X^{'}$ . Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology $σ (X^{\circ}, X)$ . We give the following application: For $Ω$ a Polish space we consider operator semigroups on the space $C_{b} (Ω)$ of bounded, continuous functions (endowed with the compact-open topology) and on the space $M (Ω)$ of bounded Baire measures (endowed with the weak $^{*}$ -topology)....

Admissible initial operators for superpositions of right invertible operators

D. Przeworska-Rolewicz (1977)

Annales Polonici Mathematici

Almost-distribution cosine functions and integrated cosine functions

Pedro J. Miana (2005)

Studia Mathematica

We introduce the notion of almost-distribution cosine functions in a setting similar to that of distribution semigroups defined by Lions. We prove general results on equivalence between almost-distribution cosine functions and α-times integrated cosine functions.