Finite rank Toeplitz operators on the Bergman space
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- by Daniel H. Luecking PDF
- Proc. Amer. Math. Soc. 136 (2008), 1717-1723 Request permission
Abstract:
Given a complex Borel measure $\mu$ with compact support in the complex plane $\mathbb {C}$ the sesquilinear form defined on analytic polynomials $f$ and $g$ by $B_\mu (f,g) = \int f\bar g d\mu$, determines an operator $T_\mu$ from the space of such polynomials $\mathcal {P}$ to the space of linear functionals on $\overline {\mathcal {P}}$. This operator is called the Toeplitz operator with symbol $\mu$. We show that $T_\mu$ has finite rank if and only if $\mu$ is a finite linear combination of point masses. Application to Toeplitz operators on the Bergman space is immediate.References
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Additional Information
- Daniel H. Luecking
- Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Ar- kansas 72701
- Email: luecking@uark.edu
- Received by editor(s): January 4, 2007
- Received by editor(s) in revised form: February 21, 2007
- Published electronically: November 30, 2007
- Communicated by: Joseph A. Ball
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1717-1723
- MSC (2000): Primary 46E20
- DOI: https://doi.org/10.1090/S0002-9939-07-09119-8
- MathSciNet review: 2373601