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A General Completion Theorem

  • C. Foias
  • A. E. Frazho
  • I. Gohberg
  • M. A. Kaashoek
Part of the Operator Theory Advances and Applications book series (OT, volume 100)

Abstract

In this chapter a general completion theorem, which may be viewed as a time-varying version of the commutant lifting theorem, is presented. Three different proofs are given. One proof uses the reduction techniques of Chapter X to convert the three chains completion theorem to a standard commutant lifting setup. The second proof goes by one step extensions, using Parrott’s lemma. The third proof gives an explicit formula for a solution which is the analogue of the central intertwining lifting. A nonstationary maximum entropy principle is given. Finally, as a first application, the three chains completion theorem is used to give a new proof of the Carswell-Schubert theorem.

Keywords

Compatibility Condition Diagonal Operator Partial Completion Commutant Lift Commutant Lift Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 1998

Authors and Affiliations

  • C. Foias
    • 1
  • A. E. Frazho
    • 2
  • I. Gohberg
    • 3
  • M. A. Kaashoek
    • 4
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Department of AeronauticsPurdue UniversityWest LafayetteUSA
  3. 3.School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityRamat AvivIsrael
  4. 4.Dept. of Mathematics and Computer ScienceVrije Universiteit AmsterdamAmsterdamThe Netherlands

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