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Journal of Operator Theory

Volume 50, Issue 2, Fall 2003  pp. 369-386.

Norms of iterates of Volterra operators on $L^2$

Authors S.P. Eveson
Author institution: Department of Mathematics, University of York, Heslington, York YO10 5DD, England UK

Summary:  It has recently been established that if $V$ is the classical Volterra (indefinite integration) operator acting on the Hilbert space $L^2([0,1])$, then the operator and Hilbert-Schmidt norms of $V^n$ are both asymptotically\break $1/(2n!)$. We extend this in two ways: firstly, we give a generalisation which applies to Volterra convolution operators with kernels satisfying a mild\break 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.

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