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Contractive completions of Hankel partial contractions
Journal article   Open access   Peer reviewed

Contractive completions of Hankel partial contractions

Raúl Curto, Carlos Hernández and Elena De Oteyza
Journal of mathematical analysis and applications, Vol.203(2), pp.303-332
1996
DOI: 10.1006/jmaa.1996.0382
url
https://doi.org/10.1006/jmaa.1996.0382View
Published (Version of record) Open Access

Abstract

A Hankel partial contraction is a Hankel matrix such that not all of its entries are determined, but in which every well-defined submatrix is a contraction. We address the problem of whether a Hankel partial contraction in which the upper left triangle is known can be completed to a contraction. It is known that the 2×2 and 3×3 cases can be solved, and that 4×4 Hankel partial contractions cannot always be completed. We introduce a technique that allows us to exhibit concrete examples of such 4×4 matrices, and to analyze in detail the dependence of the solution set on the given data. At the same time, we obtain necessary and sufficient conditions on the given cross-diagonals in order for the matrix to be completed. We also study the problem of extending a contractive Hankel block of size n to one of size n +1.

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