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arXiv · 0909.2225

Characterization of the unbounded bicommutant of C_0 (N) contractions

R. T. W. Martin
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Abstract

Recent results have shown that any closed operator $A$ commuting with the backwards shift $S^*$ restricted to $K ^2_u := H^2 \ominus u H^2$, where $u$ is an inner function, can be realized as a Nevanlinna function of $S^*_u := S^* |_{K^2_u}$, $A = φ(S^*_u)$, where $φ$ belongs to a certain class of Nevanlinna functions which depend on $u$. In this paper this result is generalized to show that given any contraction $T$ of class $C_0 (N)$, that any closed (and not necessarily bounded) operator $A$ commuting with the commutant of $T$ is equal to $φ(T)$ where $φ$ belongs to a certain class of Nevanlinna functions which depend on the minimal inner function $m_T$ of $T$.

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R. T. W. Martin. 2009-09-11. Characterization of the unbounded bicommutant of C_0 (N) contractions. https://arxiv.org/abs/0909.2225

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