Toeplitz operators on Hardy spaces with piecewise continuous symbols
The geometric descriptions of the (essential) spectra of Toeplitz operators with piecewise continuous symbols are among the most beautiful results about Toeplitz operators on Hardy spaces Hp with 1<p<∞, see . In H1, the essential spectra of Toeplitz operators are known for continuous symbols  and symbols in the Douglas algebra C+H∞ .
It is natural to ask whether the theory for piecewise continuous symbols can also be extended to the Hardy space H1. We answer this question and discuss some other related properties of Toeplitz operators on H1.
The talk is based on joint work with Santeri Miihkinen.
- A. Böttcher and Yu. I. Karlovich: Carleson curves, Muckenhoupt weights and Toeplitz operators. Springer, 1997.
- M. Papadimitrakis and J. Virtanen: Hankel and Toeplitz transforms on H1: continuity, compactness and Fredholm properties, Integr. equ. oper. theory, 61 (2008), 573-591.
- J. Virtanen, Fredholm theory of Toeplitz operators on the Hardy space H1, Bull. London Math. Soc., 38 (2006), 143-155.