Abstract
We introduce the notion of skeleton with a head in a non-zero real vector space. We prove that skeletons with a head describe order unit spaces geometrically. Next, we prove that the skeleton consists of boundary elements of the positive cone of norm one. We discuss some elementary properties of the skeleton. We also find a condition under which V contains a copy of \(\ell _{\infty }^n\) for some \(n \in {\mathbb {N}}\) as an order unit subspace.
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Acknowledgements
The author is grateful to the referee for valuable suggestions. The author was partially supported by Science and Engineering Research Board, Department of Science and Technology, Government of India sponsored Mathematical Research Impact Centric Support project (reference no. MTR/2020/000017).
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Communicated by Enrique A. Sanchez Perez.
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Karn, A.K. On the geometry of an order unit space. Adv. Oper. Theory 9, 28 (2024). https://doi.org/10.1007/s43036-024-00327-8
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DOI: https://doi.org/10.1007/s43036-024-00327-8