Proceedings of the American Mathematical Society

Author(s): M. Cabrera; J. Martínez
Journal: Proc. Amer. Math. Soc. 125 (1997), 2033-2039.
MSC (1991): Primary 47B47; Secondary 47B48, 46H05
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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 $a$

, where

denotes the centre of $A$

and

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

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