  The isospectrality problem is studied for the operator of the spherical
hydromagnetic alpha^2-dynamo. It is shown that this operator is formally
pseudo-Hermitian (J-symmetric) and lives in a Krein space. Based on the
J-symmetry, an operator intertwining Ansatz with first-order differential
intertwining operators is tested for its compatibility with the structure of
the alpha^2-dynamo operator matrix. An intrinsic structural inconsistency is
obtained in the set of associated matrix Riccati equations. This inconsistency
is interpreted as a no-go theorem which forbids the construction of isospectral
alpha^2-dynamo operator classes with the help of first-order differential
intertwining operators.
