Geometric characterization of $L_{1}$-spaces
Volume 219 / 2013
Studia Mathematica 219 (2013), 97-107
MSC: Primary 46B20; Secondary 46E30.
DOI: 10.4064/sm219-2-1
Abstract
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.
