Which weighted composition operators are complex symmetric?
Stephan Ramon Garcia, Christopher Hammond
TL;DR
This paper investigates which weighted composition operators are complex symmetric, discovering new classes of such operators and connecting their properties to normality and symmetry in operator theory.
Contribution
It identifies several new classes of complex symmetric weighted composition operators, expanding understanding of their structure and properties.
Findings
Discovered new classes of complex symmetric weighted composition operators
Established connections between normality and complex symmetry in these operators
Enhanced classification of weighted composition operators based on symmetry properties
Abstract
Recent work by several authors has revealed the existence of many unexpected classes of normal weighted composition operators. On the other hand, it is known that every normal operator is a complex symmetric operator. We therefore undertake the study of complex symmetric weighted composition operators, identifying several new classes of such operators.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Topics in Algebra · Meromorphic and Entire Functions