Journal of Operator Theory

Volume 94, Issue 1, Summer 2025 pp. 65-91.

Completely non-unitary contractions and analyticity

Authors: Susmita Das
Author institution: Indian Institute of Science, Department of Mathematics, Bangalore, 560012, India

Summary: 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 the 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~$T$.

DOI: http://dx.doi.org/10.7900/jot.2023aug23.2444
Keywords: contractions, defect spaces, unilateral shifts, analytic operators, hyponormal operators

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