In this note a commutant lifting theorem for vector-valued functional Hilbert spaces over generalized analytic polyhedra in ℂⁿ is proved. Let T be the compression of the multiplication tuple to a *-invariant closed subspace of the underlying functional Hilbert space. Our main result characterizes those operators in the commutant of T which possess a lifting to a multiplier with Schur class symbol. As an application we obtain interpolation results of Nevanlinna-Pick and Carathéodory-Fejér type for Schur class functions. Our methods apply in particular to the unit ball, the unit polydisc and the classical symmetric domains of types I, II and III.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc67-0-7,
author = {Calin Ambrozie and J\"org Eschmeier},
title = {A commutant lifting theorem on analytic polyhedra},
journal = {Banach Center Publications},
volume = {68},
year = {2005},
pages = {83-108},
zbl = {1075.47009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc67-0-7}
}
Calin Ambrozie; Jörg Eschmeier. A commutant lifting theorem on analytic polyhedra. Banach Center Publications, Tome 68 (2005) pp. 83-108. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc67-0-7/