# 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

## Abstract

We develop a complete Fredholm and invertibility theory for Toeplitz+Hankel operators $T(a)+H(b)$ on the Hardy space $\Hp$, $1<p<\iy$, with piecewise continuous functions $a,b$ defined on the unit circle which are subject to the condition $a(t)a(t\iv)=b(t)b(t\iv)$, $|t|=1$. 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