This analysis identifies properties of completely non-unitary contractions, indicating analytic behavior and eigenvalue characteristics.
We study completely non-unitary contractions T with finite dimensional defect spaces DT and DT∗. We present a complete classification of all such contractions T that satisfy a generalized property of the Hardy shift operator: DT⊆DT∗. We show that T is analytic if and only if it has no non-zero eigenvalue. Furthermore, we characterize the hyponormality of all those T.
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Susmita Das (2025) studied this question.
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