Factorization of Toeplitz and Hankel operators
Using a factorization lemma we obtain improvements and simplifications of results on representation of generalized Toeplitz and Hankel operators as compression of symbols.
Failure of Nehari's theorem for multiplicative Hankel forms in Schatten classes
Ortega-Cerdà-Seip demonstrated that there are bounded multiplicative Hankel forms which do not arise from bounded symbols. On the other hand, when such a form is in the Hilbert-Schmidt class ₂, Helson showed that it has a bounded symbol. The present work investigates forms belonging to the Schatten classes between these two cases. It is shown that for every there exist multiplicative Hankel forms in the Schatten class which lack bounded symbols. The lower bound on p is in a certain sense optimal...
Finite rank commutators of Toeplitz operators on the bidisk
We study some algebraic properties of commutators of Toeplitz operators on the Hardy space of the bidisk. First, for two symbols where one is arbitrary and the other is (co-)analytic with respect to one fixed variable, we show that there is no nontrivial finite rank commutator. Also, for two symbols with separated variables, we prove that there is no nontrivial finite rank commutator or compact commutator in certain cases.
Finite rank intermediate Hankel operators and the big Hankel operator.
Finite sections of truncated Toeplitz operators
We describe the C*-algebra associated with the finite sections discretization of truncated Toeplitz operators on the model space K2u where u is an infinite Blaschke product. As consequences, we get a stability criterion for the finite sections discretization and results on spectral and pseudospectral approximation.
Finite-rank intermediate Hankel operators on the Bergman space.
Fourier analysis of a space of Hilbert-Shmidt operators. New Ha-plitz type operators.
If a group acts via unitary operators on a Hilbert space of functions then this group action extends in an obvious way to the space of Hilbert-Schmidt operators over the given Hilbert space. Even if the action on functions is irreducible, the action on H.-S. operators need not be irreducible. It is often of considerable interest to find out what the irreducible constituents are. Such an attitude has recently been advocated in the theory of "Ha-pliz" (Hankel + Toeplitz) operators. In this paper we...
Fredholm Toeplitz operators on strongly pseudoconvex domains