On a problem of J. P. Williams
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- by Edward Kissin and Victor S. Shulman
- Proc. Amer. Math. Soc. 130 (2002), 3605-3608
- DOI: https://doi.org/10.1090/S0002-9939-02-06608-X
- Published electronically: May 8, 2002
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Abstract:
Let $B(H)$ be the algebra of all bounded operators on a Hilbert space $H$. Let $g$ be a continuous function on the closed disk $D$ and let \[ \|g(A)X - Xg(A)\| \leq C\|AX - XA\|,\] for some $C > 0,$ for all $X \in B(H)$ and all $A \in B(H)$ with $\|A\|\leq 1$. Then $g$ is differentiable on $D$. The paper shows that the function $g$ may have a discontinuous derivative.References
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Bibliographic Information
- Edward Kissin
- Affiliation: School of Communications Technology and Mathematical Sciences, University of North London, Holloway, London N7 8DB, Great Britain
- Email: e.kissin@unl.ac.uk
- Victor S. Shulman
- Affiliation: School of Communications Technology and Mathematical Sciences, University of North London, Holloway, London N7 8DB, Great Britain – and – Department of Mathematics, Vologda State Technical University, Vologda, Russia
- Email: shulman_v@yahoo.com
- Received by editor(s): March 19, 2001
- Received by editor(s) in revised form: July 6, 2001
- Published electronically: May 8, 2002
- Communicated by: David R. Larson
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3605-3608
- MSC (2000): Primary 47A56
- DOI: https://doi.org/10.1090/S0002-9939-02-06608-X
- MathSciNet review: 1920040