Journal of the Iranian Mathematical Society

Journal of the Iranian Mathematical Society

On some properties of neutral SFS-spaces

Document Type : Research Article

Authors
J. K. Seypullaev 1
A. D. Arziev 2
K. Kalenbaev 2
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.
10.30504/jims.2024.480745.1208
Abstract
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.
Keywords
Geometric tripotent
norm exposed face
strongly facially symmetric space
Subjects
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Journal of the Iranian Mathematical Society
Volume 5, Issue 2
March 2024
Pages 261-269