Description of facially symmetric spaces with unitary tripotents

Abstract

We give a description of finite-dimensional real neutral strongly facially symmetric spaces with the property JP. We also prove that if \(Z\) is a real neutral strongly facially symmetric with an unitary tripotents, then the space \(Z\) is isometrically isomorphic to the space \(L_1(\Omega,\Sigma, \mu),\) where \((\Omega,\Sigma, \mu)\) is a measure space having the direct sum property.