Projective positivity of the function systems

Abstract 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 positivit...
Ausführliche Beschreibung

Abstract 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 %$L^{p} %$-spaces, Schatten matrix spaces, and %$L^{p}%$-spaces of a finite von Neumann algebra. Ausführliche Beschreibung