Journal of Operator Theory

Volume 58, Issue 1, Summer 2007 pp. 157-173.

Compact tripotents and the Stone-Weierstrass Theorem for

$C^*$ -algebras and JB

$^*$ -triples

Authors: Francisco J. Fern\'{a}ndez-Polo (1) and Antonio M. Peralta (2)
Author institution: (1) Departamento de An\'{a}lisis Matem\'{a}tico, Facultad de Ciencias, Universidad de Granada, Granada, 18071, Spain
(2) Departamento de An\'{a}lisis Matem\'{a}tico, Facultad de Ciencias, Universidad de Granada, Granada, 18071, Spain

Summary: We establish some generalizations of Urysohn lemma for the \textit{hull-kernel structure} in the setting of JB

$^*$ -triples. These results are the natural extensions of those obtained by C.A. Akemann in the setting of

$C^*$ -algebras. We also develop some connections with the classical Stone-Weierstrass problem for

$C^*$ -algebras and JB

$^*$ -triples.

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