Dual Toeplitz Operators on the Sphere
Dual Toeplitz operators on the Hardy space of the unit circle are anti-unitarily equivalent
to Toeplitz operators. In higher dimensions, for instance on the unit sphere, dual Toeplitz operators
might behave quite differently and, therefore, seem to be a worth studying new class of Toeplitz-type
operators. The purpose of this paper is to introduce and start a systematic investigation of dual Toeplitz
operators on the orthogonal complement of the Hardy space of the unit sphere in Cn. In particular, we
establish a corresponding spectral inclusion theorem and a Brown–Halmos type theorem. On the other
hand, we characterize commuting dual Toeplitz operators as well as normal and quasinormal ones.
In this paper we use the Duhamel product to provide a Banach algebra structure to each of a scale of Bergman spaces over the unit disk, and then carry out many interesting consequences.
We characterize skew-symmetric operators on a reproducing kernel Hilbert space in terms of their
Berezin symbols. The solution of some operator equations with skew-symmetric operators is…