Algebras of truncated Toeplitz operators
N.A. Sedlock
TL;DR
This paper characterizes when the product of two truncated Toeplitz operators remains within the same class, providing a complete description of maximal algebras of bounded truncated Toeplitz operators.
Contribution
It establishes necessary and sufficient conditions for the product of two truncated Toeplitz operators to be a truncated Toeplitz operator, and characterizes maximal algebras of these operators.
Findings
Identified conditions for operator products to stay within the algebra
Characterized maximal algebras of bounded truncated Toeplitz operators
Provided a complete algebraic structure for these operators
Abstract
We find necessary and sufficient conditions for the product of two truncated Toeplitz operators on a model space to itself be a truncated Toeplitz operator, and as a result find a characterization for the maximal algebras of bounded truncated Toeplitz operators.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Topics in Algebra · Advanced Operator Algebra Research