On the density of Toeplitz operators in the Toeplitz algebra over the Bergman space of the unit ball
Vishwa Dewage, Mishko Mitkovski
TL;DR
This paper offers a new proof that Toeplitz operators are dense in the Toeplitz algebra over the Bergman space of the unit ball, utilizing quantum harmonic analysis and representation theory.
Contribution
It introduces a novel proof method for Xia's theorem, expanding the theoretical understanding of Toeplitz operators in complex analysis.
Findings
Toeplitz operators are norm dense in the Toeplitz algebra
New proof employs quantum harmonic analysis and representation theory
Enhances theoretical framework of operator density in Bergman spaces
Abstract
We use quantum harmonic analysis and representation theory to provide a new proof of Xia's theorem: "Toeplitz operators are norm dense in the Toeplitz algebra over the Bergman space of the unit ball."
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Topics in Algebra · Algebraic and Geometric Analysis