Geodesic
Simplex algebras and their representation
Glasgow mathematical journal, Tome 14 (1973) no. 2, pp. 136-144

Voir la notice de l'article provenant de la source Cambridge University Press

This paper establishes a relationship (Theorem 4.1) between the approaches of A. C. Thompson [8, 9] and E. G. Effros [2] to the representation of simplex algebras, that is, real unital Banach algebras that are simplex spaces with the unit for order identity. It proves that the (nonempty) interior of the associated cone is contained in the principal component of the set of all regular elements of the algebra. It also conjectures that each maximal ideal (in the order sense—see below) of a simplex algebra contains a maximal left ideal of the algebra. This conjecture and other aspects of the relationship are illustrated by considering algebras of n × n real matrices. 
Vijayakumar, M. S. Simplex algebras and their representation. Glasgow mathematical journal, Tome 14 (1973) no. 2, pp. 136-144. doi: 10.1017/S0017089500001889
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