Vol. 69, No. 2, 1977

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Riesz homomorphisms and positive linear maps

Charles Thomas Tucker, II

Vol. 69 (1977), No. 2, 551–556

It was shown in previous papers [C. T. Tucker, “Homomorphisms of Riesz spaces,” Pacific J. Math., 55 (1974), 289–300, and “Concerning σ-homomorphisms of Riesz spaces,” Pacific J. Math., 57 (1975), 585–590] that there is a large class β of Riesz spaces with the property that if L belongs to β and ϕ is a Riesz homomorphism of L into an Archimedean Riesz space then ϕ preserves the order limit of sequences. In this paper it is shown that if L belongs to β then every order bounded linear map of L into an Archimedean, directed, partially ordered vector space is sequentially continuous. An application of this is made to the theory of Baire funtions. Further, some properties of those members of β which are also normed Riesz spaces are considered.

Mathematical Subject Classification 2000
Primary: 47B55, 47B55
Secondary: 46A40
Received: 6 April 1976
Revised: 1 November 1976
Published: 1 April 1977
Charles Thomas Tucker, II