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Some Remarks on Talenti's Semigroup
Published online by Cambridge University Press: 20 November 2018
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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 > 0, if limh→0I(α+h)x =I(α)x, ∀x ∊ X.
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- Copyright © Canadian Mathematical Society 1971
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