  In 1999, Grunbaum, Haine and Horozov defined a large family of commutative
algebras of ordinary differential operators which have orthogonal polynomials
as eigenfunctions. These polynomials are mutually orthogonal with respect to a
Laguerre-type weight distribution, thus providing solutions to Krall's problem.
In the present paper we give a new proof of their result which establishes a
conjecture, concerning the explicit characterization of the dual commutative
algebra of eigenvalues. In particular, for the Koornwinder's generalization of
Laguerre polynomials, our approach yields an explicit set of generators for the
whole algebra of differential operators. We also illustrate how more general
Sobolev-type orthogonal polynomials fit within this theory.
