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A Commutant Lifting Theorem for a Domain in ℂ2 and Spectral Interpolation

Lookup NU author(s): Professor Jim Agler, Emeritus Professor Nicholas Young

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Abstract

We characterise the pairs of commuting operators on Hilbert space for which the domain Γ = {(λ1 + λ2, λ1λ2): |λ1| ≤ 1, |λ2| ≤ 1} is a complete spectral set. We give an application to the spectral Nevanlinna-Pick problem: we obtain a necessary condition for the existence of an analytic 2 × 2 matrix function satisfying interpolation conditions and bounds on eigenvalues. © 1999 Academic Press.

Publication metadata

Author(s): Agler J, Young NJ

Publication type: Article

Publication status: Published

Journal: Journal of Functional Analysis

Year: 1999

Volume: 161

Issue: 2

Pages: 452-477

Print publication date: 01/02/1999

ISSN (print): 0022-1236

ISSN (electronic): 1096-0783

Publisher: Academic Press

URL: http://dx.doi.org/10.1006/jfan.1998.3362

DOI: 10.1006/jfan.1998.3362

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