Geodesic
Geometric characterization of $L_{1}$-spaces
Normuxammad Yadgorov1 ; Mukhtar Ibragimov2 ; Karimbergen Kudaybergenov2
1 National University of Uzbekistan Vuzgorodok, 100174, Tashkent, Uzbekistan
2 Karakalpak State University 230113 Nukus, Uzbekistan
Studia Mathematica, Tome 219 (2013) no. 2, pp. 97-107

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The paper is devoted to a description of all real 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.
DOI : 10.4064/sm219-2-1
Keywords: paper devoted description real strongly facially symmetric spaces which isometrically isomorphic spaces prove real neutral strongly facially symmetric space every maximal geometric tripotent dual space unitary space isometrically isomorphic space omega sigma where omega sigma appropriate measure space having direct sum property

Normuxammad Yadgorov 1 ; Mukhtar Ibragimov 2 ; Karimbergen Kudaybergenov 2

1 National University of Uzbekistan Vuzgorodok, 100174, Tashkent, Uzbekistan
2 Karakalpak State University 230113 Nukus, Uzbekistan 
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Normuxammad Yadgorov; Mukhtar Ibragimov; Karimbergen Kudaybergenov. Geometric characterization of $L_{1}$-spaces. Studia Mathematica, Tome 219 (2013) no. 2, pp. 97-107. doi: 10.4064/sm219-2-1

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