Operator residuation in orthomodular posets of finite height

We show that for every orthomodular poset P=(P,≤,′,0,1) of finite height there can be defined two operators forming an adjoint pair with respect to order-like relation on the power set P. This enables us introduce so-called operator residuated corresponding P from which original recovered. this construction applied also weakly and dually posets. Examples such posets are included.