Norms of Iterates of Volterra Operators on L^2

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It has recently been established that if V is the classical Volterra (indefinite integration) operator acting on the Hilbert space L2([0, 1]), then the operator and Hilbert-Schmidt norms of V n are both asymptotically 1/(2n!). We extend this in two ways: firstly, we give a generalisation which applies to Volterra convolution operators with kernels satisfying a mild smoothness condition, and secondly we show that in the constant-kernel case the same asymptotic behaviour is shared by the trace norm, and hence by a wide class of operator norms.
Original languageEnglish
Pages (from-to)369-386
Number of pages17
JournalJournal of Operator Theory
Issue number2
Publication statusPublished - 2003


  • Volterra operators

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