JournalsjstVol. 3, No. 2pp. 171–214

Fredholm and invertibility theory for a special class of Toeplitz + Hankel operators

  • Estelle L. Basor

    American Institute of Mathematics, Palo Alto, USA
  • Torsten Ehrhardt

    University of California at Santa Cruz, USA
Fredholm and invertibility theory for a special class of Toeplitz + Hankel operators cover
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Abstract

We develop a complete Fredholm and invertibility theory for Toeplitz+Hankel operators T(a)+H(b)T(a)+H(b) on the Hardy space \Hp\Hp, 1<p<\iy1<p<\iy, with piecewise continuous functions a,ba,b defined on the unit circle which are subject to the condition a(t)a(t\iv)=b(t)b(t\iv)a(t)a(t\iv)=b(t)b(t\iv), t=1|t|=1. In particular, in the case of Fredholmness, formulas for the defect numbers are established. The results are applied to several important examples.

Cite this article

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. 171–214

DOI 10.4171/JST/42