THE RELATIONSHIP BETWEEN BASE NORM SPACES AND STRONGLY FACIALLY SYMMETRIC SPACES

This paper considers the connection between base norm spaces and strongly facially symmetric spaces (SFS-spaces). We investigate the geometric properties of the unit ball in an SFS-space and show that they can be described as base-norm spaces generated by a cone, whose base is a symmetric face possessing a Jordan decomposition. Additionally, we study unitarily geometric tripotents in real SFS-spaces, where under certain conditions these spaces become base norm spaces. The results obtained contribute to a better understanding of SFS-spaces and their role in the axiomatic study of quantum mechanics.