Characterization of the Unbounded Bicommutant of C0(n) Contractions

Abstract

Recent results have shown that any closed operator A commuting with the backwards shift S∗ restricted to K u := H 2 ⊖ uH, where u is an inner function, can be realized as a Nevanlinna function of S∗ u := S ∗| K2 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 C0(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 mT of T .

Cite this paper

@inproceedings{Martin2009CharacterizationOT, title={Characterization of the Unbounded Bicommutant of C0(n) Contractions}, author={Tod Martin}, year={2009} }