A commutant lifting theorem on analytic polyhedra

Calin Ambrozie, and Jörg Eschmeier. "A commutant lifting theorem on analytic polyhedra." Banach Center Publications 67.1 (2005): 83-108. <http://eudml.org/doc/282287>.

@article{CalinAmbrozie2005,
abstract = {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 $M_z$ 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.},
author = {Calin Ambrozie, Jörg Eschmeier},
journal = {Banach Center Publications},
keywords = {commutant lifting; vector-valued functional Hilbert spaces; Schur class; Carathéodory–Fejér interpolation},
language = {eng},
number = {1},
pages = {83-108},
title = {A commutant lifting theorem on analytic polyhedra},
url = {http://eudml.org/doc/282287},
volume = {67},
year = {2005},
}

TY - JOUR
AU - Calin Ambrozie
AU - Jörg Eschmeier
TI - A commutant lifting theorem on analytic polyhedra
JO - Banach Center Publications
PY - 2005
VL - 67
IS - 1
SP - 83
EP - 108
AB - 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 $M_z$ 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.
LA - eng
KW - commutant lifting; vector-valued functional Hilbert spaces; Schur class; Carathéodory–Fejér interpolation
UR - http://eudml.org/doc/282287
ER -