TY - JOUR T1 - Isometric representations of calibrated ordered spaces on $C(X)$ AU - Ay, Serdar PY - 2025 DA - September Y2 - 2025 DO - 10.31801/cfsuasmas.1582901 JF - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics JO - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. PB - Ankara University WT - DergiPark SN - 1303-5991 SP - 523 EP - 545 VL - 74 IS - 3 LA - en AB - The problem of characterizing normed ordered spaces which admit a representation in the algebraic, order and norm sense as a subspace of $C(X)$, the space of all continuous functions on a compact Hausdorff space is a classical problem that has been considered by many authors. In this article we consider the more general case of calibrated ordered spaces, that is, ordered spaces with a specified family of seminorms generating its topology. For such spaces equivalent conditions on representability as a subspace of $C(X)$ for some locally compact Hausdorff space $X$, in the algebraic, order and seminorm sense are stated and proved. Some characterizations appear to be new even in the normed case. A recent result on isometric representations of locally ordered spaces fall under the results in this paper with more general statements. As an application of the main theorems, we state and prove a characterization of norm additivity property of two positive functionals. KW - Calibrated ordered space KW - representation of an ordered space KW - locally Riesz space KW - Schaefer’s construction KW - BNN extension CR - Aliprantis, C. D., Tourky, R., Cones and Duality, AMS Graduate Studies in Mathematics 84, 2007. CR - Allan, G. R., On a class of locally convex algebras, Proc. Lond. Math. Soc., 15 (1965), 399-421. CR - Apostol, C., $b^*$-Algebras and their representations, J. London Math. Soc., 33 (1971), 30-38. CR - Asadi, M. 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I., Sharipov, F., Hilbert modules over locally $C^*$-algebras, (2001), arXiv:math/0011053v3. UR - https://doi.org/10.31801/cfsuasmas.1582901 L1 - https://dergipark.org.tr/en/download/article-file/4355649 ER -