Geometric characterization of L₁-spaces

Normuxammad Yadgorov, Mukhtar Ibragimov, and Karimbergen Kudaybergenov. "Geometric characterization of L₁-spaces." Studia Mathematica 219.2 (2013): 97-107. <http://eudml.org/doc/285516>.

@article{NormuxammadYadgorov2013,
abstract = {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.},
author = {Normuxammad Yadgorov, Mukhtar Ibragimov, Karimbergen Kudaybergenov},
journal = {Studia Mathematica},
keywords = {facially symmetric space; tripotent; unitary; L1-space},
language = {eng},
number = {2},
pages = {97-107},
title = {Geometric characterization of L₁-spaces},
url = {http://eudml.org/doc/285516},
volume = {219},
year = {2013},
}

TY - JOUR
AU - Normuxammad Yadgorov
AU - Mukhtar Ibragimov
AU - Karimbergen Kudaybergenov
TI - Geometric characterization of L₁-spaces
JO - Studia Mathematica
PY - 2013
VL - 219
IS - 2
SP - 97
EP - 107
AB - 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.
LA - eng
KW - facially symmetric space; tripotent; unitary; L1-space
UR - http://eudml.org/doc/285516
ER -