# A commutant lifting theorem on analytic polyhedra

Calin Ambrozie; Jörg Eschmeier

Banach Center Publications (2005)

- Volume: 67, Issue: 1, page 83-108
- ISSN: 0137-6934

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topCalin 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 -

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