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Bulletin of the London Mathematical Society Advance Access originally published online on May 3, 2008
Bulletin of the London Mathematical Society 2008 40(3):493-504; doi:10.1112/blms/bdn038
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© 2008 London Mathematical Society

On the level sets of the resolvent norm of a linear operator

E. Shargorodsky

Department of Mathematics
King's College London
Strand
London
WC2R 2LS
United Kingdom

Received 2 October 2007. Revision received 7 February 2008.

We construct a bounded linear operator on a Banach space and a closed densely defined operator on a Hilbert space with resolvent norms that are constant in a neighbourhood of zero. We also discuss cases where the norm of the resolvent of a bounded linear operator cannot be constant on an open set.

2000 Mathematics Subject Classification 47A10.


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