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A Time-variant Norm Constrained Interpolation Problem Arising from Relaxed Commutant Lifting

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Operator Algebras, Operator Theory and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 195))

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Abstract

A time-variant analogue of an interpolation problem equivalent to the relaxed commutant lifting problem is introduced and studied. In a somewhat less general form the problem already appears in the analysis of the set of all solutions to the three chain completion problem. The interpolants are upper triangular operator matrices of which the columns induce contractive operators. The set of all solutions of the problem is described explicitly. The results presented are time-variant analogues of the main theorems in [23].

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Author information

Authors and Affiliations

  1. Department of Aeronautics and Astronautics, Purdue University, West Lafayette, IN, 47907, USA

    A. E. Frazho

  2. Department of Mathematics, Utrecht University, Budapestlaan 6, NL-3584 CD, Utrecht, The Netherlands

    S. ter Horst

  3. Afdeling Wiskunde, Faculteit der Exacte Wetenschappen, Vrije Universiteit, De Boelelaan 1081a, NL-1081 HV, Amsterdam, The Netherlands

    M. A. Kaashoek

Authors
  1. A. E. Frazho
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  2. S. ter Horst
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  3. M. A. Kaashoek
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Editor information

Editors and Affiliations

  1. School for Computer, Statistical and Mathematical Sciences, North-West University, 2520, Potchefstroom, South Africa

    J. J. Grobler

  2. Department of Mathematical Sciences, University of South Africa, PO Box 392, 0003 UNISA, South Africa

    L. E. Labuschagne

  3. John Knopfmacher Centre for Applicable Analysis and Number Theory School of Mathematics, University of the Witwatersrand, 2050 WITS, South Africa

    M. Möller

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Frazho, A.E., ter Horst, S., Kaashoek, M.A. (2009). A Time-variant Norm Constrained Interpolation Problem Arising from Relaxed Commutant Lifting. In: Grobler, J.J., Labuschagne, L.E., Möller, M. (eds) Operator Algebras, Operator Theory and Applications. Operator Theory: Advances and Applications, vol 195. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0174-0_6

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