When products of selfadjoints are normal
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- by E. Albrecht and P. G. Spain PDF
- Proc. Amer. Math. Soc. 128 (2000), 2509-2511 Request permission
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?References
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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
- Received by editor(s): November 15, 1999
- Published electronically: April 11, 2000
- Communicated by: David R. Larson
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2509-2511
- MSC (2000): Primary 46H99; Secondary 47B15, 47B40
- DOI: https://doi.org/10.1090/S0002-9939-00-05830-5
- MathSciNet review: 1756087