Calkin Representations of Unbounded Operator Algebras Acting on Non‐Separable Domains

There are constructed representations of unbounded operator algebras which generalize representations of B ( H ) constructed by J. W. CALKIN and H. BEHNCKE. For a large class of unitary spaces D , each uniformly closed two‐sided ideal of the maximal Op *‐algebra L + ( D ) appears as kernel of such a representation. Irreducibility of the representations is characterized in terms of properties of ultrafilters which define the representations.