On subspaces of an intermediate characteristic in $C^*$

With the approximate solution of integral equations, the regularizability of the inverse mapping plays a leading role. If the inverse mapping is regularizable, then the equation can be solved by Tikhonov's method. Otherwise the regularization method is not applicable. In 1978, L.D. Menikhes built an example of integral mapping such the inverse mapping is nonregularizable. As follows from the work of V.A. Vinokurov et al. regularizability is closely related to the characteristic (index) of the image of the conjugate operator. If this characteristic is nonzero, then the inverse of the integral mapping is regularizable. The purpose of this paper is to propose a method for constructing subspaces in $C^*$ with a non-trivial (intermediate between 0 and 1) characteristic.