On the general intertwining lifting problem. I

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http://pub.acta.hu/acta/showCustomerArticle.action?id=4253&dataObjectType=article&returnAction=showCustomerVolume&sessionDataSetId=1998750858719eb8&style=

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UMBC Mathematics and Statistics Department

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https://orcid.org/0000-0001-8594-0568

Date

2005-11-08

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journal articles
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Biswas, Animikh, and Ciprian Foias. “On the General Intertwining Lifting Problem. I,” Acta Sci. Math. (Szeged), 72, no. 1 (2006): 271-298. http://pub.acta.hu/acta/showCustomerArticle.action?id=4253&dataObjectType=article&returnAction=showCustomerVolume&sessionDataSetId=1998750858719eb8&style=

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Abstract

We consider the general intertwining lifting problem as formulated in [F1] and which is connected to interpolation problems in reproducing kernel Hilbert spaces. We reduce this general problem to the case where the operators involved are nn block upper-triangular. As a consequence, we show that the causal commutant lifting (see [FT]) and the general intertwining lifting (or extension) problems are equivalent. We also obtain a seemingly new commutant lifting result for the case where one of the operators involved is nilpotent and the other canonical block Jordan. Finally, as an application, we obtain a completely new proof for the Ceausescu--Carswell--Schubert result (see [Ce], [CaS]).