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On the Schur Representation in the Commutant Lifting Theorem II

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Topics in Operator Theory and Interpolation

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 29))

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Abstract

This note is a continuation of [4]. Here we present a short proof of the fact that the Schur representation formula presented in [4] yields all contractive intertwining dilations in the Commutant Lifting Theorem.

We dedicate this note to Professor M.S. Livsic on the occassion of his 70th birthday. He was the first to use linear functional representations in modelling operators.

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References

  1. Arsene, Gr., Z. Ceausescu, and C. Foias. On intertwining dilations VIII. J. Operator Theory, 4 (1980), pp. 55–91.

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  2. Arsene, Gr. and A. Gheondea. Completing matrix contractions. J. Operator Theory, 7 (1982) pp. 179–189.

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  3. Foias, C. Contractive intertwining dilations and waves in layered media. Proceedings on the International Congress of Mathematicians. Helsinki (1978), Vol. 2, pp. 605–613.

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  4. Foias, C. and A.E. Frazho. On the Schur representation in the Commutant Lifting Theorem I. Operator Theory Advances and Applications I.Schur Methods in Operator Theory and signal processing Edited by I. Gohberg (1986), pp. 207–217.

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  5. S. Parrott, On a quotient norm and the Sz.-Nagy-Foias lifting theorem, J. Fund. Analysis, 30 (1978), pp. 311–328.

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  6. Sz.-Nagy, B. and C. Foias. Harmonic analysis of operators on Hilbert space, Amsterdam-Budapest, 1970.

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  7. Sz.-Nagy, B. and C. Foias. Dilation des communtants. C.R. Acad. Sei. Paris, Serie A, 266 (1968) pp. 493–495.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Indiana University, Bloomington, Indiana, 47401, USA

    Ciprian Foias

  2. School of Aeronautics and Astronautics, Purdue University, West Lafayette, Indiana, 47907, USA

    Arthur E. Frazho

Authors
  1. Ciprian Foias
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  2. Arthur E. Frazho
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

    I. Gohberg

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© 1988 Birkhäuser Verlag Basel

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Foias, C., Frazho, A.E. (1988). On the Schur Representation in the Commutant Lifting Theorem II. In: Gohberg, I. (eds) Topics in Operator Theory and Interpolation. Operator Theory: Advances and Applications, vol 29. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9162-2_7

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  • DOI: https://doi.org/10.1007/978-3-0348-9162-2_7

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-7643-1960-1

  • Online ISBN: 978-3-0348-9162-2

  • eBook Packages: Springer Book Archive

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