Norms of Iterates of Volterra Operators on L^2

S. Eveson

Norms of Iterates of Volterra Operators on L^2

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	369-386
Number of pages	17
Journal	Journal of Operator Theory
Volume	50
Issue number	2
Publication status	Published - 2003

Keywords

Volterra operators

Cite this

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abstract = "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.",

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T1 - Norms of Iterates of Volterra Operators on L^2

AU - Eveson, S.

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AB - 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.

KW - Volterra operators

M3 - Article

SN - 1841-7744

VL - 50

SP - 369

EP - 386

JO - Journal of Operator Theory

JF - Journal of Operator Theory

IS - 2

ER -