On a paper by Gesztesy, Simon, and Teschl concerning isospectral deformations of ordinary Schrödinger operators

Starting from a selfadjoint Schrödinger operator A=−d2/dx2 + q with a gap G in its spectrum F. Gesztesy, B. Simon, G. Teschl [J. Analyse Math. 70 (1996) 267–324] succeed in constructing another Schrödinger operator A˜ = −d2/dx2 + ˜q that is unitarily equivalent (and thus isospectral) to A. As the means they apply come from the Weyl–Titchmarsh theory the connections prove to be intricate, in particular the relation between A and A˜.We show that a central assertion in GST’s paper rests substantially on factorizations of the form (A− μ)(A− ν) = B∗B, A˜B = BA, μ, ν being numbers in G and B an invertible 2nd order differential operator generated by corresponding eigensolutions of A. Hence A˜ = UAU∗ where U is the unitary operator B|B|−1. The operators B and U do not occur explicitly in F. Gesztesy, B. Simon, G. Teschl [J. Analyse Math. 70 (1996) 267–324].  2002 Elsevier Science (USA). All rights reserved.