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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A remark on commuting operator exponentials


Author: Edgar M. E. Wermuth
Journal: Proc. Amer. Math. Soc. 125 (1997), 1685-1688
MSC (1991): Primary 39B42, 47A60, 30E10
MathSciNet review: 1353407
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Abstract: In a previous paper the author proved that for square matrices with algebraic entries exp$(A)$exp$(B)=$exp$(B)$exp$(A)$ if and only if $AB=BA$. This result is extended here to bounded operators on an arbitrary Banach space.


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Additional Information

Edgar M. E. Wermuth
Affiliation: Zentralinstitut für Angewandte Mathematik, Forschungszentrum Jülich GmbH, Postfach 1913, D-52425 Jülich, Germany
Address at time of publication: FB Allgemeinwissenschaften und Informatik, Georg-Simon-Ohm-FH Nürnberg, Postfach 210320, D-90121 Nürnberg, Germany
Email: e.m.e.wermuth@kfa-juelich.de, edgar.wermuth@ai.fh-nuernberg.de

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03643-5
PII: S 0002-9939(97)03643-5
Keywords: Commuting exponentials, Dunford's integral, Runge's theorem
Received by editor(s): May 9, 1995
Received by editor(s) in revised form: September 6, 1995
Additional Notes: For valuable comments I thank Heinrich Bock, Robert B. Burckel, Hans-Günter Meier, and the referee.
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1997 American Mathematical Society