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Geometric characterization of $L_{1}$-spaces

Tom 219 / 2013

Normuxammad Yadgorov, Mukhtar Ibragimov, Karimbergen Kudaybergenov Studia Mathematica 219 (2013), 97-107 MSC: Primary 46B20; Secondary 46E30. DOI: 10.4064/sm219-2-1

Streszczenie

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.

Autorzy

  • Normuxammad YadgorovNational University of Uzbekistan
    Vuzgorodok, 100174, Tashkent, Uzbekistan
    e-mail
  • Mukhtar IbragimovKarakalpak State University
    230113 Nukus, Uzbekistan
    e-mail
  • Karimbergen KudaybergenovKarakalpak State University
    230113 Nukus, Uzbekistan
    e-mail

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