Subordination for Balayage Spaces

Let X be a Iccb space, Uand W two sub-Markov resolvents on X possessing proper potential kernels U and V such that W is subordinated to U (i. e. V_λ ≤ U_λ Vλ]0, ∞[). Denote by S _U , S _W respectively E _U E` _W the cone of super-median respectively excessive functions associated with U and W. The purpose of this article is: (i) to study the situation where (X, E _U ) and (X, E _W ) are both balayage spaces (in the sense of [3]) and P is the sub-Markov kernel on X satisfying U=V+PU, and (ii) to give conditions on U, V and P under which (X, E _W ) respectively (X, E _U ) form a balayage space, provided (X, E _U ) respectively (X, E _W ) is a balayage space. The notations are the notations of [3].