An example on ordered Banach algebras
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- by Gerd Herzog and Christoph Schmoeger PDF
- Proc. Amer. Math. Soc. 135 (2007), 3949-3954 Request permission
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 $K=\{(a,\xi ) \in {\mathcal A}: \|a\| \le \xi \}$, and investigate the connection between results on ordered Banach algebras and the right bound of the numerical range of elements in ${\mathcal B}$.References
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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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 3949-3954
- MSC (2000): Primary 47H05, 47A12, 47B60
- DOI: https://doi.org/10.1090/S0002-9939-07-09000-4
- MathSciNet review: 2341945