The Volterra operator is finitely strictly singular from L1 to L^\infty

Pascal Lefèvre (1)

1 LML - Laboratoire de Mathématiques de Lens

We show that the Volterra operator viewed from L1([0; 1]) to C([0; 1]) is finitely strictly singular. Actually we estimate the Bernstein numbers and show that their asymptotic growth is 1/2n in the case of real valued functions. The same ideas apply to the summation operator.

Mots clés: Volterra; Finitely strictly singular; Bernstein numbers

Domaines: Analyse fonctionnelle [math.FA]

Pascal Lefèvre. The Volterra operator is finitely strictly singular from L1 to L^\infty. 2016. ⟨hal-01315503v2⟩