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

 

Inner derivations
on ultraprime normed algebras


Authors: M. Cabrera and J. Martínez
Journal: Proc. Amer. Math. Soc. 125 (1997), 2033-2039
MSC (1991): Primary 47B47; Secondary 47B48, 46H05
MathSciNet review: 1389506
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Abstract: We show that, for every ultraprime Banach algebra $A$, there exists a positive number $\gamma $ satisfying $\gamma \|a+Z(A)\|\le \|D_a\|$ for all $a$ in $A$, where $Z(A)$ denotes the centre of $A$ and $D_a$ denotes the inner derivation on $A$ induced by $a$. Moreover, the number $\gamma $ depends only on the ``constant of ultraprimeness'' of $A$.


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Additional Information

M. Cabrera
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain
Email: cabrera@goliat.ugr.es

J. Martínez
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain
Email: jmmoreno@goliat.ugr.es

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03833-1
PII: S 0002-9939(97)03833-1
Received by editor(s): September 26, 1995
Received by editor(s) in revised form: January 24, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society