Abstract of a paper by Normuxammad Yadgorov, Mukhtar Ibragimov, and Karimbergen Kudaybergenov
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 or http://arXiv.org/abs/1311.4429
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