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Lobachevskii Journal of Mathematics, vol.44, no.6, pp.2007-2019, 2023 (ESCI)
Abstract: The present paper is devoted to the local projective positivity in the category of the local function systems or commutative local operator systems. The local projective positivity reflects the local positivity occurred in the quantizations of a projective local function system. We prove that every *-polynormed topology compatible with a duality results in the local projective positivity given by a filter base of the unital cones with its separated intersection. It allows to describe the local projective positivity of the local Lp -spaces given by a bounded or unbounded positive Radon measure on a locally compact topological space.