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We consider the Banach-Mackey property for pairs of vector spaces E and E which are in duality. Let A be an algebra of sets and assume that P is an additive map from A into the projection operators on E. We define a continuous gliding hump property for the map P and show that pairs with this gliding hump property and another measure theoretic property are Banach-Mackey pairs, i. e., weakly bounded subsets of E are strongly bounded. Examples of vector valued function spaces, such as the space ofdoi:10.4067/s0716-09172001000200007 fatcat:re2yzloppbdkjanzfnw24jzlou