Let T be the Volterra operator on L2[0, 1]
where f∈L2[0, 1], 0[les ]x[les ]1. It is well known that ∥n!Tn∥=O(1/n!). In a recent paper , D. Kershaw has proved that
a result which was first conjectured by Lao and Whitley in . It is easy to prove that
For completeness, we give the proof using the familiar Schmidt norm estimate for the norm of an integral operator (see Section 2 below). Kershaw proves that
by analysing the special positivity preserving properties of T*T. He uses one of the many abstract theorems on eigenvalues and eigenfunctions of compact operators which preserve a cone. In this paper we shall reprove (1), giving a short and direct proof of (2).
Email your librarian or administrator to recommend adding this journal to your organisation's collection.