We develop a complete Fredholm and invertibility theory for Toeplitz+Hankel operators on the Hardy space \( \Hp \), \( 1<p<\iy \), with piecewise continuous functions defined on the unit circle which are subject to the condition \( a(t)a(t\iv)=b(t)b(t\iv) \), . In particular, in the case of Fredholmness, formulas for the defect numbers are established. The results are applied to several important examples.
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Estelle L. Basor, Torsten Ehrhardt, Fredholm and invertibility theory for a special class of Toeplitz + Hankel operators. J. Spectr. Theory 3 (2013), no. 2, pp. 171–214DOI 10.4171/JST/42