The paper is devoted to a description of all real strongly facially symmetric spaces which are isometrically isomorphic to L₁-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 L₁(Ω,Σ,μ), where (Ω,Σ,μ) is an appropriate measure space having the direct sum property.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm219-2-1,
author = {Normuxammad Yadgorov and Mukhtar Ibragimov and Karimbergen Kudaybergenov},
title = {Geometric characterization of L1-spaces},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {97-107},
zbl = {06238585},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm219-2-1}
}
Normuxammad Yadgorov; Mukhtar Ibragimov; Karimbergen Kudaybergenov. Geometric characterization of L₁-spaces. Studia Mathematica, Tome 215 (2013) pp. 97-107. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm219-2-1/