Some Remarks on Talenti's Semigroup

Abstract

Let X be a Banach space. Consider the family I(α) of linear continuous operators from X into itself, depending on the parameter α ≥ 0. Suppose that I(α1+α2)=I(α1)I(α2)∀α1, α2 ≥ 0 and I(0)=I (semigroupal property). Such a semigroup is said to be strongly continuous for α &gt; 0, if limh→0I(α+h)x =I(α)x, ∀x ∊ X.</jats:p