Duality in the space of regulated functions and the play operator

As a new weak convergence concept motivated originally by singular perturbation problems, we investigate the wbo-convergence in the space of regulated functions with values in a Hilbert space. Using a generalization of the Tvrdý Representation Theorem for bounded linear functionals on the space of regulated functions, we establish the relationship between the weak and the wbo-con vergences. The classical play operator from the mathematical theory of hysteresis is used as an important tool in the analysis.