- December 5, 2008 , Friday - 15h00 (Room P
3.10):
Connectedness of spectra of Toeplitz operators
on Hardy spaces with Muckenhoupt weights over Carleson curves
Alexei Karlovich
(Universidade Nova de Lisboa and CEAF, IST, UT Lisboa)
Abstract. 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 > 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 > 1,
with
general Muckenhoupt weights w over arbitrary Carleson
curves G. This is a
joint work with Ilya Spitkovsky.
Seminars take place in Lisbon, I.S.T. -
Post Graduation Building
Webpage: http://www.math.ist.utl.pt/funcional
