A commutant lifting theorem on analytic polyhedra

• Autorzy: Calin Ambrozie , Jörg Eschmeier
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A57: Operator methods in interpolation, moment and extension problems
• 47A13: Several-variable operator theory (spectral, Fredholm, etc.)
• 41A05: Interpolation
• 47A20: Dilations, extensions, compressions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2005
• Tom: 67
• Numer: 1
• Strony: 83-108

Daty

wydano

2005

Twórcy

autor

Calin Ambrozie

• Institute of Mathematics, Romanian Academy, PO Box 1-764, 70700 Bucharest, Romania

autor

Jörg Eschmeier

• Fachrichtung Mathematik, Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany

Identyfikatory

DOI

10.4064/bc67-0-7