Functional Analysis and Applications Seminar 

05/12/2008, 15:00 — 16:00 — Room P3.10, Mathematics Building
Alexei Karlovich, Universidade Nova de Lisboa and CEAF, IST, UT Lisboa

Connectedness of spectra of Toeplitz operators on Hardy spaces with Muckenhoupt weights over Carleson curves

Harold Widom proved in 1966 that the spectrum of a Toeplitz operator $T(a)$ acting on the Hardy space $H^p(T)$ over the unit circle $T$ is a connected subset of the complex plane for every bounded measurable symbol $a$ and $p \gt 1$. In 1972, Ronald Douglas established the connectedness of the essential spectrum of $T(a)$ on $H^2(T)$. We show that, as was suspected, these results remain valid in the setting of Hardy spaces $H^p(G,w), p \gt 1,$ with general Muckenhoupt weights $w$ over arbitrary Carleson curves $G$. This is a joint work with Ilya Spitkovsky.