Invertibility issues for Toeplitz plus Hankel operators and their close relatives (Q1980910)

In the paper the authors describes various approaches to the invertibility of Toeplitz plus Hankel operators in Hardy and \(l_{p}\)-spaces, integral and difference Wiener-Hopf plus Hankel operators and generalized Toeplitz plus Hankel operators. First they make a brief presentation of the classical approach of I. Gohberg, N. Krupnik and G. Litvinchuk, as well as, Basor-Ehrhardt Approach. A second large presentation is dedicated to a recently newly method developed by the authors of the paper. Not all proofs of the results are given. The interested readers can consult the paper for more details. For the entire collection see [Zbl 1471.47002].