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When products of selfadjoints are normal

Author(s): E. Albrecht; P. G. Spain
Journal: Proc. Amer. Math. Soc. 128 (2000), 2509-2511.
MSC (2000): Primary 46H99; Secondary 47B15, 47B40
Posted: April 11, 2000
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Abstract:

Suppose that $ h, \, k \in \mathcal{L}(\mathcal{H})$ are two selfadjoint bounded operators on a Hilbert space $\mathcal{H}$. It is elementary to show that $hk$ is selfadjoint precisely when $hk = kh$. We answer the following question: Under what circumstances must $hk$ be selfadjoint given that it is normal?

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Additional Information:

E. Albrecht
Affiliation: Fachbereich 9 Mathematik, Universität des Saarlandes, Postfach 151150, 66041 Saarbrücken, Germany
Email: ernstalb@math.uni-sb.de

P. G. Spain
Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland
Email: pgs@maths.gla.ac.uk

DOI: 10.1090/S0002-9939-00-05830-5
PII: S 0002-9939(00)05830-5
Keywords: Hilbert space, operator, normal, selfadjoint, hermitian, numerical range, Banach algebra
Received by editor(s): November 15, 1999
Posted: April 11, 2000
Communicated by: David R. Larson
Copyright of article: Copyright 2000, American Mathematical Society

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