Little, G.; Reade, J. B. Estimates for the norm of the \(n\)th indefinite integral. (English) Zbl 0931.47032 Bull. Lond. Math. Soc. 30, No. 5, 539-542 (1998). A Volterra operator \[ Tf(x)= \int^x_0 f(t) dt \] is considered, where \(f\in L^2[0,1]\), \(0\leq x\leq 1\).Recently, D. Kersaw [Integral Equations Appl., to appear] has proved the following property of the norm of \(T\) in \(L^2(0, 1)\) \[ \lim_{n\to\infty}\|n! T^n\|={1\over 2}.\tag{1} \] The authors present a short and direct proof of the inequality \[ \lim_{n\to\infty}\inf\|n! T^n\|\geq {1\over 2}.\tag{2} \] The inequality \[ \lim_{n\to\infty}\sup\|n! T^n\|\leq{1\over 2} \] provides the easer part of the proof of (1). Reviewer: D.Przeworska-Rolewicz (Warszawa) Cited in 12 Documents MSC: 47G10 Integral operators 45D05 Volterra integral equations 45P05 Integral operators 47A30 Norms (inequalities, more than one norm, etc.) of linear operators Keywords:Volterra operator PDFBibTeX XMLCite \textit{G. Little} and \textit{J. B. Reade}, Bull. Lond. Math. Soc. 30, No. 5, 539--542 (1998; Zbl 0931.47032) Full Text: DOI