On some properties of neutral SFS-spaces
نویسندگان
1 Department of Mathematics, Karakalpak State University named after Berdakh, P.O.Box 230112, Nukus, Uzbekistan.
2 V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, P.O.Box 100174, Tashkent, Uzbekistan.
3 V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, P.O.Box 100174, Tashkent, Uzbekistan.
doi
10.30504/jims.2024.480745.1208چکیده
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.
