Iranian Mathematical Society Journal of the Iranian Mathematical Society 2717-1612 5 2 2024 03 01 On some properties of neutral SFS-spaces 261 269 209800 10.30504/jims.2024.480745.1208 EN J. K. Seypullaev Department of Mathematics, Karakalpak State University named after Berdakh, P.O.Box 230112, Nukus, Uzbekistan. 0000-0003-2938-2199 A. D. Arziev V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, P.O.Box 100174, Tashkent, Uzbekistan. 0000-0001-6137-6819 K. Kalenbaev V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, P.O.Box 100174, Tashkent, Uzbekistan. 0009-0004-9388-3945 Journal Article 2024 09 28 One of the important problems of the operator algebras theory is the geometric characterization of state spaces of operator algebras‎. ‎In this regard‎, ‎in mid-1980s‎, ‎a paper by Friedman and Russo introduced facially symmetric spaces‎. ‎The primary aim of this work was to provide the geometric characterization of predual spaces of $JBW^\ast$-triples that possess an algebraic structure‎. ‎Many of the properties required in these characterizations are natural assumptions for the state spaces of physical systems‎. ‎Such spaces are considered as a geometric model for the states of quantum mechanics‎. ‎In this paper, we show that if any indecomposable geometric tripotent‎ ‎of a neutral strongly facially symmetric space is a minimal geometric tripotent then any extreme point is a norm exposed point‎. ‎Moreover‎, ‎in an atomic neutral locally base normed strongly facially symmetric space any extreme point is a norm exposed point‎. ‎We also prove that every real neutral strongly facially symmetric space with unitary tripotents is finite‎. https://jims.ims.ir/article_209800_d1c9e2a8f5bfe16c8597281569c5ae68.pdf