Journal article
A NEW NECESSARY CONDITION FOR THE HYPONORMALITY OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE
Journal of operator theory, Vol.79(2), pp.287-300
03/01/2018
DOI: 10.7900/jot.2017feb15.2152
Abstract
A well known result of C. Cowen states that, for a symbol phi is an element of L-infinity, phi (math) (f) over bar + g (f, g, is an element of H-2), the Toeplitz operator T-phi, acting on the Hardy space of the unit circle is hyponormal if and only if f = c + T(<()(h))(over bar>)g, for some c is an element of C, h is an element of H-infinity), parallel to h parallel to(infinity) <= 1. In this note we consider possible versions of this result in the Bergman space case. Concretely, we consider Toeplitz operators on the Bergman space of the unit disk, with symbols of the form
phi (math) alpha z(n) + beta z(m) + gamma(z) over bar (p) + delta(z) over bar (q),
where alpha, beta, gamma, delta is an element of C and m, n, p, q is an element of Z(+), m < n and p < q. By studying the asymptotic behavior of the action of T-phi, on a particular sequence of vectors, we obtain a sharp inequality involving the above mentioned data. This inequality improves a number of existing results, and it is intended to be a precursor of basic necessary conditions for joint hyponormality of tuples of Toeplitz operators acting on Bergman spaces in one or several complex variables.
Details
- Title: Subtitle
- A NEW NECESSARY CONDITION FOR THE HYPONORMALITY OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE
- Creators
- Zeljko Cuckovic - Univ Toledo, Dept Math, Toledo, OH 43606 USARaul E Curto - Univ Iowa, Dept Math, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Journal of operator theory, Vol.79(2), pp.287-300
- Publisher
- THETA FOUNDATION
- DOI
- 10.7900/jot.2017feb15.2152
- ISSN
- 0379-4024
- eISSN
- 1841-7744
- Number of pages
- 14
- Grant note
- DMS-0801168; DMS-1302666 / U.S. NSF
- Language
- English
- Date published
- 03/01/2018
- Academic Unit
- Mathematics
- Record Identifier
- 9984241152902771
Metrics
26 Record Views