This is an announcement for the paper "Geometric characterization of $L_1$-spaces" by Normuxammad Yadgorov, Mukhtar Ibragimov, and Karimbergen Kudaybergenov.
Abstract: The paper is devoted to a description of all strongly facially symmetric spaces which are isometrically isomorphic to $L_1$-spaces. We prove that if $Z$ is a real neutral strongly facially symmetric space such that every maximal geometric tripotent from the dual space of $Z$ is unitary then, the space $Z$ is isometrically isomorphic to the space $L_1(\Omega, \Sigma, \mu),$ where $(\Omega, \Sigma, \mu)$ is an appropriate measure space having the direct sum property.
Archive classification: math.OA
Mathematics Subject Classification: 46B20
Remarks: Accepted to publication in the journal Studia Mathematica
Submitted from: karim20061@yandex.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.4429
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