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

 

An example on ordered Banach algebras


Authors: Gerd Herzog and Christoph Schmoeger
Journal: Proc. Amer. Math. Soc. 135 (2007), 3949-3954
MSC (2000): Primary 47H05, 47A12, 47B60
Published electronically: September 7, 2007
MathSciNet review: 2341945
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Abstract: Let $ {\mathcal B}$ be a complex unital Banach algebra. We consider the Banach algebra $ {\mathcal A}={\mathcal B} \times \mathbb{C}$ ordered by the algebra cone $ K=\{(a,\xi) \in {\mathcal A}: \Vert a\Vert \le \xi\}$, and investigate the connection between results on ordered Banach algebras and the right bound of the numerical range of elements in $ {\mathcal B}$.


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Additional Information

Gerd Herzog
Affiliation: Institut für Analysis, Universität Karlsruhe, D-76128 Karlsruhe, Germany
Email: Gerd.Herzog@math.uni-karlsruhe.de

Christoph Schmoeger
Affiliation: Institut für Analysis, Universität Karlsruhe, D-76128 Karlsruhe, Germany
Email: christoph.schmoeger@math.uni-karlsruhe.de

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09000-4
PII: S 0002-9939(07)09000-4
Keywords: Ordered Banach algebras, bounds of numerical range, fractional powers.
Received by editor(s): September 22, 2006
Received by editor(s) in revised form: November 6, 2006
Published electronically: September 7, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.