On p-convexification of the Banach-Kantorovich lattice

Let B be a complete Boolean algebra, Q(B) the Stone compact of B, and let C∞(Q(B)) be the commutative unital algebra of all continuous functions x:Q(B)→[−∞,+∞], assuming possibly the values ±∞ on nowhere-dense subsets of Q(B). Let (E,∥⋅∥E )⊂C∞ (Q(B)) be a Banach-Kantorovich lattice over the algebra L0(Ω) of equivalence classes of almost everywhere finite real-valued measurable functions on a measurable space (Ω,Σ,μ) with σ-finite measure μ. The paper defines the p-convexification of the Banach-Kantorovich lattice (E,∥⋅∥E ) and proves that it is also a Banach-Kantorovich lattice over L0(Ω).