Contractive liftings and the commutator
[Dilatations contractive et le commutateur]
Foias, Ciprian1, 2 ; Frazho, Arthur E.3 ; Kaashoek, Marinus A.4
1 Texas A&M University, College Station, TX 77843, USA
2 Indiana University, Bloomington, IN 47405-5701, USA
3 School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907-1282, USA
4 Divisie Wiskunde en Informatica, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
Comptes Rendus. Mathématique, Tome 335 (2002) no. 5, pp. 431-436.

Cet article présente la solution d'un problème posé par B.Sz.-Nagy sur l'extension du théorème de dilatation des commutants au cas des opérateurs sous-jacents qui ne commutent pas. Le théorème principal établit des dilatations aux normes minimales de certains commutateurs. La démonstration est constructive.

This paper presents the solution to a problem proposed by B.Sz.-Nagy about extending the commutant lifting theorem to the case when the underlying operators do not intertwine. The main theorem establishes minimal norm liftings of certain commutators. The proof is constructive.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02508-6
Foias, Ciprian 1, 2 ; Frazho, Arthur E. 3 ; Kaashoek, Marinus A. 4

1 Texas A&M University, College Station, TX 77843, USA
2 Indiana University, Bloomington, IN 47405-5701, USA
3 School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907-1282, USA
4 Divisie Wiskunde en Informatica, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands 
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Foias, Ciprian; Frazho, Arthur E.; Kaashoek, Marinus A. Contractive liftings and the commutator. Comptes Rendus. Mathématique, Tome 335 (2002) no. 5, pp. 431-436. doi : 10.1016/S1631-073X(02)02508-6. http://www.numdam.org/articles/10.1016/S1631-073X(02)02508-6/

[1] Foias, C.; Frazho, A.E. The Commutant Lifting Approach to Interpolation Problems, Operator Theory: Advances and Applications, 44, Birkhäuser, Basel, 1990

[2] Foias, C.; Frazho, A.E.; Gohberg, I.; Kaashoek, M.A. Metric Constrained Interpolation, Commutant Lifting and Systems, Operator Theory: Advances and Applications, 100, Birkhäuser, Basel, 1998

[3] Foias, C.; Frazho, A.E.; Kaashoek, M.A. Relaxation of metric constrained interpolation and a new lifting theorem, Integral Equations Operator Theory, Volume 42 (2002), pp. 253-310

[4] Sarason, D. Generalized interpolation in H∞, Trans. Amer. Math. Soc., Volume 127 (1967), pp. 179-203

[5] Sz.-Nagy, B.; Foias, C. Dilatation des commutants d'opérateurs, C. R. Acad. Sci. Paris, Série A, Volume 266 (1968), pp. 493-495

[6] B. Sz.-Nagy, Personal communication, 1968

[7] Sz.-Nagy, B.; Foias, C. Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam–Budapest, 1970

[8] Treil, S.; Volberg, A. A fixed point approach to Nehari's problem and its applications, Toeplitz Operators and Related Topics. The Harold Widom Anniversary Volume, OT 71, Birkhäuser, Basel, 1994, pp. 165-186

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