The central intertwining lifting

and strict contractions

Author:
Radu Gadidov

Journal:
Proc. Amer. Math. Soc. **124** (1996), 3813-3817

MSC (1991):
Primary 47A20; Secondary 47A57

DOI:
https://doi.org/10.1090/S0002-9939-96-03540-X

MathSciNet review:
1346972

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we give a necessary and sufficient condition for the central intertwining lifting of a strict contraction to be strictly contractive. As an application, we obtain a factorization of when the central intertwining lifting of is a strict contraction.

**1.**V.M. Adamjan, D.Z. Arov, and M.G. Krein,*Infinite Hankel block matrices and related extension problems*, Izv. Akad. Nauk. Armyan SSR.,**6**(1971), pp. 87-112; English transl., Amer. Math. Soc. Transl.**111**(1978), pp. 136-156. MR**45:7506****2.**M. Bakonyi,*A remark on Nehari's problem*, Integral Equations Operator Theory**22**(1995), 123-125. MR**95m:47017****3.**C. Foias and A. E. Frazho,*The Commutant Lifting Approach to Interpolation Problems*, Birkhaüser Verlag, Basel, 1990. MR**92k:47033****4.**C. Foias and A. E. Frazho,*Commutant lifting and simultaneous*, SIAM J. Math. Anal.,**H**and**L**suboptimization**23**(1992), pp. 984-994. MR**93e:47011****5.**C. Foias, A. E. Frazho, and W. S. Li,*The exact*, Operator Theory: Adv. and Appl., vol. 64, (1993), pp. 119-156. MR**H**estimate for the central**H**interpolants**95e:47019****6.**A. E. Frazho,*A four block approach to central commutant lifting*, Indiana Univ. Math. J.,**42**(1993), pp. 821-838. MR**94j:47010****7.**B. Sz.-Nagy and C. Foias,*Dilatation des commutants d'operateurs*, C. R. Acad. Sci. Paris, Sér. A,**266**(1968), pp. 493-495. MR**38:5049****8.**B. Sz.-Nagy and C. Foias,*Harmonic analysis of operators on Hilbert space*, North-Holland, Amsterdam, 1970. MR**43:947****9.**N. K. Nikol'skii,*Treatise on the shift operator*, Lecture Notes in Math., vol.**273**Springer-Verlag Berlin New-York, 1980. MR**87i:47042**

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Additional Information

**Radu Gadidov**

Affiliation:
Institute of Mathematics of Romanian Academy, Box 1-764, RO-70700 Bucharest, Romania

Address at time of publication:
Department of Industrial Engineering, Texas A&M University, College Station, Texas 77843

Email:
gadidov@integer.tamu.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03540-X

Received by editor(s):
February 21, 1995

Received by editor(s) in revised form:
June 20, 1995

Additional Notes:
This paper was presented at the 1995 GPOTS Conference held in Cincinnati.

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1996
American Mathematical Society