Toeplitz plus Hankel operators with infinite index
We will consider Toeplitz plus Hankel operators generated by symbols which have points of standard almost periodic discontinuities, and acting between Lebesgue spaces. Conditions are obtained under which these operators are right-invertible and with infinite kernel dimension, left-invertible and with infinite cokernel dimension or simply not normally solvable. This will be done by employing a certain real functional, looking to the resulting signs on the points of standard almost periodic discontinuities. Examples will be provided to illustrate the obtained results.
