Distance entre éléments d'un semi-groupe dans une algébre de Banach. (Distance between the elements of a semigroup in a Banach algebra)
Consider a semigroup \((a^t)_{t>0}\) in a Banach algebra. Let \(n\) be a positive integer. The best possible constant \(C(n)\) is obtained such that if \(\limsup_{t\to 0^+}\|a^{t}-a^{t(n+1)}\|< C(n)\), then either \(a^t = 0\) for \(t>0\), or the closed algebra \(A\) generated by the semigroup \((a^t)\) is unital and there exists \(u\in A\) such that \(a^t = e^{tu}\) for \(t > 0\).
scientific article; zbMATH DE number 1888345
scientific article