Characteristic functions and Colligations
Neeru Bala, Santanu Dey, Reshmi M. N
TL;DR
This paper explores the use of colligations to analyze characteristic functions of row contractions and their liftings, providing new proofs, characterizations, and transformations related to these mathematical objects.
Contribution
It offers alternative proofs for invariance properties, characterizes a class of co-isometric colligations, and studies Blaschke factor transformations of characteristic functions.
Findings
Characteristic functions are complete invariants for row contractions and their liftings.
A class of co-isometric observable colligations with finite-dimensional input spaces is characterized.
Blaschke factor transformations of characteristic functions are analyzed.
Abstract
The characteristic function of row contractions and liftings of row contractions are complete invariants up to unitary equivalence for row contractions and liftings of row contractions, respectively. We provide alternate proofs for these using colligations. A class of co-isometric observable colligations with input spaces of finite dimension is characterized. Blaschke factor based transformations of the characteristic function of lifting are studied.
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Taxonomy
TopicsControl and Stability of Dynamical Systems · Advanced Operator Algebra Research · Advanced Topics in Algebra