Some Remarks on Talenti's Semigroup

Some Remarks on Talenti's Semigroup

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→0 I(α+h)x =I(...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Canadian mathematical bulletin 1971-06, Vol.14 (2), p.147-150
1. Verfasser: Chrysovergis, A.
Format: Artikel
Sprache:eng
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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→0 I(α+h)x =I(α)x, ∀x ∊ X.
ISSN:0008-4395
1496-4287
DOI:10.4153/CMB-1971-027-0