Isospectrality of spherical MHD dynamo operators:: Pseudo-hermiticity and a no-go theorem

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. (C) 2003 American Institute of Physics.