Positivity, vol.27, no.4, 2023 (SCI-Expanded)
Article / Article
Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Business Source Elite, Business Source Premier, MathSciNet, zbMATH
Function system, Operator system, Projective positivity, State space, Unital cone
Middle East Technical University Affiliated:
The present paper is devoted to the projective positivity in the category of function systems, which plays a key role in the quantization problems of the operator systems. The main result of the paper asserts that every unital ∗ -normed space can be equipped with the projective positivity. The geometry of the related state spaces is described in the case of Lp -spaces, Schatten matrix spaces, and Lp -spaces of a finite von Neumann algebra.