Trace Formula of Semicommutators
Xiang Tang, Yi Wang, Dechao Zheng
TL;DR
This paper derives trace formulas for semicommutators of Toeplitz operators on weighted Bergman spaces, extending the results to higher dimensions and exploring applications to Hankel operators.
Contribution
It introduces a generalized trace formula for semicommutators of Toeplitz operators on weighted Bergman spaces in multiple dimensions.
Findings
Derived trace formulas for semicommutators of Toeplitz operators.
Extended formulas to higher-dimensional weighted Bergman spaces.
Discussed applications to Hankel operators.
Abstract
For weighted Bergman spaces on the unit disk, we give trace formulas of semicommutators of Toeplitz operators with symbols. We generalize this formula to weighted Bergman spaces on the unit ball in higher dimensions. Applications and examples on the Hankel operators are also discussed.
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Taxonomy
TopicsHolomorphic and Operator Theory · Algebraic and Geometric Analysis · Advanced Topics in Algebra