Duality, Tangential Interpolation, and Töplitz Corona Problems

Mrinal Raghupathi; Brett D. Wick

doi:10.1007/s00020-010-1802-y

Duality, Tangential Interpolation, and Töplitz Corona Problems

Mrinal Raghupathi
, Brett D. Wick

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this paper, we extend a method of Arveson (J Funct Anal 20(3):208-233, 1975) and McCullough (J Funct Anal 135(1):93-131, 1996) to prove a tangential interpolation theorem for subalgebras of H^∞. This tangential interpolation result implies a Töplitz corona theorem. In particular, it is shown that the set of matrix positivity conditions is indexed by cyclic subspaces, which is analogous to the results obtained for the ball and the polydisk algebra by Trent and Wick (Complex Anal Oper Theory 3(3):729-738, 2009) and Douglas and Sarkar (Proc CRM, 2009).

Original language	English
Pages (from-to)	337-355
Number of pages	19
Journal	Integral Equations and Operator Theory
Volume	68
Issue number	3
DOIs	https://doi.org/10.1007/s00020-010-1802-y
State	Published - Nov 2010

Keywords

Distance formulae
Hilbert module
Nevanlinna-Pick interpolation
Toeplitz corona problem

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title = "Duality, Tangential Interpolation, and T{\"o}plitz Corona Problems",

abstract = "In this paper, we extend a method of Arveson (J Funct Anal 20(3):208-233, 1975) and McCullough (J Funct Anal 135(1):93-131, 1996) to prove a tangential interpolation theorem for subalgebras of H∞. This tangential interpolation result implies a T{\"o}plitz corona theorem. In particular, it is shown that the set of matrix positivity conditions is indexed by cyclic subspaces, which is analogous to the results obtained for the ball and the polydisk algebra by Trent and Wick (Complex Anal Oper Theory 3(3):729-738, 2009) and Douglas and Sarkar (Proc CRM, 2009).",

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AU - Raghupathi, Mrinal

AU - Wick, Brett D.

PY - 2010/11

Y1 - 2010/11

N2 - In this paper, we extend a method of Arveson (J Funct Anal 20(3):208-233, 1975) and McCullough (J Funct Anal 135(1):93-131, 1996) to prove a tangential interpolation theorem for subalgebras of H∞. This tangential interpolation result implies a Töplitz corona theorem. In particular, it is shown that the set of matrix positivity conditions is indexed by cyclic subspaces, which is analogous to the results obtained for the ball and the polydisk algebra by Trent and Wick (Complex Anal Oper Theory 3(3):729-738, 2009) and Douglas and Sarkar (Proc CRM, 2009).

AB - In this paper, we extend a method of Arveson (J Funct Anal 20(3):208-233, 1975) and McCullough (J Funct Anal 135(1):93-131, 1996) to prove a tangential interpolation theorem for subalgebras of H∞. This tangential interpolation result implies a Töplitz corona theorem. In particular, it is shown that the set of matrix positivity conditions is indexed by cyclic subspaces, which is analogous to the results obtained for the ball and the polydisk algebra by Trent and Wick (Complex Anal Oper Theory 3(3):729-738, 2009) and Douglas and Sarkar (Proc CRM, 2009).

KW - Distance formulae

KW - Hilbert module

KW - Nevanlinna-Pick interpolation

KW - Toeplitz corona problem

UR - https://www.scopus.com/pages/publications/78149500008

U2 - 10.1007/s00020-010-1802-y

DO - 10.1007/s00020-010-1802-y

M3 - Article

AN - SCOPUS:78149500008

SN - 0378-620X

VL - 68

SP - 337

EP - 355

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 3

ER -

Duality, Tangential Interpolation, and Töplitz Corona Problems

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Keywords

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