Abstract
The main result of this paper puts forward a class of morphisms of H-cones, possessing image: namely those commuting with arbitrary infimum. Applying this result to the canonical embedding in the bidual, one gets a decomposition of any H-cone In the particular case when the cone has the specific order, this decomposition gives a well-known theorem of Dixmier [1], on the structure of stonian compact spaces.
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References
J. Dixmier, Sur certains espaces considérés par M.H. Stone, Summa Bras. Math. 151, 1951.
N. Boboc, Gh. Bucur, A. Cornea, Order and Convexity in Potential Theory: H-cones, Lecture Notes in Mathematics, vol. 853, Springer-Verlag, 1981.
N. Boboc, Gh. Bucur, Stonian Structures in Potential Theory, Preprint INCREST, Bucureşti, 52/1984.
E. Popa, Morphisms of H-cones, An. Şt. Univ. Iasi, t. XXIX, f. 2 (1983).
E. Popa, Morphisms of H-cones and Semi-polar Sets, An. Şt. Univ. Iaşi, t. XXX, f. 3 (1984).
E. Popa, Finely Open Morphisms of H-cones, Math. Ann. 270 (1985).
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© 1988 Plenum Press, New York
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Popa, E. (1988). Morphisms of Stonian Cones. In: Král, J., Lukeš, J., Netuka, I., Veselý, J. (eds) Potential Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0981-9_35
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DOI: https://doi.org/10.1007/978-1-4613-0981-9_35
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