Conversely given a representation of the Weyl commutation relations on H , it gives rise to a non-degenerate representation of the *-algebra of kernel operators. But all such representations are on an orthogonal direct sum of copies of L (R) with the action on each copy as above. This is a straightforward generalisation of the elementary fact that the representations of the N × N matrices are on direct sums of the standard representation on C. The proof using matrix units works equally well in infinite dimensions.