 The theorem, proved by Richard Kadison, was surprising as "a priori" there is no reason to believe that all topologically irreducible representations are also algebraically irreducible.A family formula_1 of bounded operators on a Hilbert space formula_2 is said to act "topologically irreducibly" when formula_3 and formula_2 are the only closed stable subspaces under formula_1.The family formula_1 is said to act "algebraically irreducibly" if formula_3 and formula_2 are the only linear manifolds in formula_2 stable under formula_1.