Relaxed commutant lifting: existence of a unique solution
S. ter Horst
TL;DR
This paper establishes necessary and sufficient conditions for the existence of a unique solution to the relaxed commutant lifting problem, revealing more complex criteria than classical cases and simplifying under special circumstances.
Contribution
It provides a comprehensive characterization of when a unique solution exists in the relaxed commutant lifting problem, extending classical results.
Findings
Necessary and sufficient conditions for unique solutions
Conditions are more complex than classical cases
Simplifications occur in special cases
Abstract
In this paper we present necessary and sufficient conditions for the existence of a unique solution to the relaxed commutant lifting problem. The obtained conditions are more complicated than those for the classical commutant lifting setting, and earlier obtained sufficient conditions turn out not to be necessary conditions. It is also shown that these conditions simplify in certain special cases.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Holomorphic and Operator Theory · Geometric and Algebraic Topology