Geodesic
An Extension of the Concept of the Order Dual of a Riesz Space
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 488-498

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

Let L be a σ-Dedekind complete Riesz space. In (8), H. Nakano uses an extension of the multiplication operator on a Riesz space into itself (analagous to the closed operator on a Hilbert space) to obtain a representation space for the Riesz space L. He calls such an operator a “dilatator operator on L.” More specifically, he shows that the set of all dilatator operators , when suitable operations are defined, is a Dedekind complete Riesz space which is isomorphic to the space of all functions defined and continuous on an open dense subset of some fixed totally disconnected Hausdorff space. The embedding of L in the function space is then obtained by showing that L is isomorphic to a Riesz subspace of . Moreover, when L is Dedekind complete, it is an ideal in , and the topological space is extremally disconnected. 
Luxemburg, W. A. J.; Masterson, J. J. An Extension of the Concept of the Order Dual of a Riesz Space. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 488-498. doi: 10.4153/CJM-1967-041-6
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