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# 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)
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.