On a problem of J. P. Williams

Authors:
Edward Kissin and Victor S. Shulman

Journal:
Proc. Amer. Math. Soc. **130** (2002), 3605-3608

MSC (2000):
Primary 47A56

DOI:
https://doi.org/10.1090/S0002-9939-02-06608-X

Published electronically:
May 8, 2002

MathSciNet review:
1920040

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be the algebra of all bounded operators on a Hilbert space . Let be a continuous function on the closed disk and let

for some for all and all with . Then is differentiable on . The paper shows that the function may have a discontinuous derivative.

**1.**D. R. Jocic,*Integral representation formula for generalized normal derivation*, Proc. Amer. Math. Soc.**127**(1999), 2303-2314. MR**99j:47026****2.**B. E. Johnson and J. P. Williams,*The range of a normal derivation*, Pacific J. Math.**58**(1975), 105-122. MR**52:1390****3.**E. Kissin and V. S. Shulman,*Classes of Operator-smooth Functions.*I.*Operator Lipschitz Functions*, preprint, (2000).**4.**T. W. Palmer,*Banach Algebras and the General Theory of -algebras*, vol. I, CUP, 1994. MR**95c:46002****5.**R. Powers,*A remark on the domain of an unbounded derivation of a -algebra*, J. Funct. Anal.**18**(1975), 85-95. MR**52:1334****6.**B. Sz.-Nagy and C. Foias,*Analyse Harmonique des Operateurs de l'espace de Hilbert*, Academiai Kiado, Budapest, 1967. MR**37:778****7.**J. P. Williams,*Derivation ranges*:*open problems*, Topics in Modern Operator Theory, (Timisoara/Herculane, 1980), 319-328, Operator Theory: Adv. Appl., 2, Birkhäuser, Basel-Boston, MA, 1981. MR**83k:47027**

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Additional 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

DOI:
https://doi.org/10.1090/S0002-9939-02-06608-X

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

Article copyright:
© Copyright 2002
American Mathematical Society