Completely non unitary contractions and Analyticity

Susmita Das

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arXiv · 2307.12373

Completely non unitary contractions and Analyticity

Susmita Das

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Abstract

We study completely non-unitary contractions $T$ with finite dimensional defect spaces $\mathcal{D}_T$ and $\mathcal{D}_{T^*}$. We present a complete classification of all such contractions $T$ that satisfy a generalized property of Hardy shift operator: $\mathcal{D}_T\subseteq\mathcal{D}_{T^*}$. 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. 2023-07-23. Completely non unitary contractions and Analyticity. https://arxiv.org/abs/2307.12373

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