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Journal Articles Journal of Operator Theory Year : 2020

Interpolation without commutants

Oleg Szehr
  • Function : Author
Rachid Zarouf


We introduce a "dual-space approach" to mixed Nevanlinna-Pick/Carathéodory-Schur interpolation in Banach spaces X of holomorphic functions on the disk. Our approach can be viewed as complementary to the well-known commutant lifting approach of D. Sarason and B. Nagy-C.Foiaş. We compute the norm of the minimal interpolant in X by a version of the Hahn-Banach theorem, which we use to extend functionals defined on a subspace of kernels without increasing their norm. This Functional extensions lemma plays a similar role as Sarason's Commutant lifting theorem but it only involves the predual of X and no Hilbert space structure is needed. As an example, we present the respective Pick-type interpolation theorems for Beurling-Sobolev spaces.
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Dates and versions

hal-02898954 , version 1 (14-07-2020)



Oleg Szehr, Rachid Zarouf. Interpolation without commutants. Journal of Operator Theory, inPress, 84 (1), pp.18. ⟨10.7900/jot.2019may21.2264⟩. ⟨hal-02898954⟩
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