Gleason's problem and Schur multipliers in the multivariable quaternionic setting

Khaled Abu-Ghanem; Daniel Alpay; Fabrizio Colombo; Irene Sabadini

doi:10.1016/j.jmaa.2015.01.022

Gleason's problem and Schur multipliers in the multivariable quaternionic setting

Khaled Abu-Ghanem, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Department of Mathematics

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

10 Scopus citations

Abstract

We define and study the counterparts of Gleason's problem, of the Drury-Arveson's space and of Schur multipliers when the unit ball of CN is replaced by the unit ball of HN, where H denotes the algebra of real quaternions. Schur multipliers are characterized in terms of coisometric operator matrices in quaternionic spaces. Finally, we define the counterpart of Blaschke factors in this setting and study a one point interpolation problem.

Original language	English
Pages (from-to)	1083-1096
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	425
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2015.01.022
State	Published - 15 May 2015

Keywords

Gleason's problem
Quaternionic Drury-Arveson
Realizations
Schur multipliers
Several quaternionic variables

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2015.01.022

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abstract = "We define and study the counterparts of Gleason's problem, of the Drury-Arveson's space and of Schur multipliers when the unit ball of CN is replaced by the unit ball of HN, where H denotes the algebra of real quaternions. Schur multipliers are characterized in terms of coisometric operator matrices in quaternionic spaces. Finally, we define the counterpart of Blaschke factors in this setting and study a one point interpolation problem.",

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AU - Abu-Ghanem, Khaled

AU - Alpay, Daniel

AU - Colombo, Fabrizio

AU - Sabadini, Irene

PY - 2015/5/15

Y1 - 2015/5/15

N2 - We define and study the counterparts of Gleason's problem, of the Drury-Arveson's space and of Schur multipliers when the unit ball of CN is replaced by the unit ball of HN, where H denotes the algebra of real quaternions. Schur multipliers are characterized in terms of coisometric operator matrices in quaternionic spaces. Finally, we define the counterpart of Blaschke factors in this setting and study a one point interpolation problem.

AB - We define and study the counterparts of Gleason's problem, of the Drury-Arveson's space and of Schur multipliers when the unit ball of CN is replaced by the unit ball of HN, where H denotes the algebra of real quaternions. Schur multipliers are characterized in terms of coisometric operator matrices in quaternionic spaces. Finally, we define the counterpart of Blaschke factors in this setting and study a one point interpolation problem.

KW - Gleason's problem

KW - Quaternionic Drury-Arveson

KW - Realizations

KW - Schur multipliers

KW - Several quaternionic variables

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VL - 425

SP - 1083

EP - 1096

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Gleason's problem and Schur multipliers in the multivariable quaternionic setting

Abstract

Keywords

ASJC Scopus subject areas

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