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THE NORM OF POWERS OF THE INDEFINITE INTEGRAL OPERATOR ON (0, 1)

Published online by Cambridge University Press:  01 September 1998

B. THORPE
B. THORPE
Affiliation:
School of Mathematics and Statistics, The University of Birmingham, Birmingham B15 2TT
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Abstract

In this paper we find the norm of powers of the indefinite integral operator V, acting on L2(0, 1). This answers a question raised by Halmos, and supplements some recent results of Manakov in [9]. Using results of Stepanov in [13], we show that the operator norm of Vn is asymptotically equal to the Hilbert–Schmidt norm as n→∞.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 5 , September 1998 , pp. 543 - 548
Copyright
© The London Mathematical Society 1998

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