A strong Parrott theorem
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- by Ciprian Foias and Allen Tannenbaum PDF
- Proc. Amer. Math. Soc. 106 (1989), 777-784 Request permission
Abstract:
In this note we discuss a strengthened version of a theorem due to Parrott [8] in operator dilation theory. We relate our result to the one-step extension procedure of Adamjan-Arov-Krein [1].References
- V. M. Adamjan, D. Z. Arov, and M. G. Kreĭn, Analytic properties of the Schmidt pairs of a Hankel operator and the generalized Schur-Takagi problem, Mat. Sb. (N.S.) 86(128) (1971), 34–75 (Russian). MR 0298453
- Chandler Davis, A factorization of an arbitrary $m\times n$ contractive operator-matrix, Toeplitz centennial (Tel Aviv, 1981) Operator Theory: Advances and Applications, vol. 4, Birkhäuser, Basel-Boston, Mass., 1982, pp. 217–232. MR 669910
- Chandler Davis, W. M. Kahan, and H. F. Weinberger, Norm-preserving dilations and their applications to optimal error bounds, SIAM J. Numer. Anal. 19 (1982), no. 3, 445–469. MR 656462, DOI 10.1137/0719029
- Harry Dym and Israel Gohberg, A maximum entropy principle for contractive interpolants, J. Funct. Anal. 65 (1986), no. 1, 83–125. MR 819176, DOI 10.1016/0022-1236(86)90018-2
- Ciprian Foias and Arthur E. Frazho, Redheffer products and the lifting of contractions on Hilbert space, J. Operator Theory 11 (1984), no. 1, 193–196. MR 739802 C. Foias and A. Tannenbaum, On the singular values of the four block operator and certain generalized interpolation problems, invited paper for a volume dedicated to Professor Mischa Cotlar on his seventy-fifth birthday, 1988.
- Bruce A. Francis, A course in $H_\infty$ control theory, Lecture Notes in Control and Information Sciences, vol. 88, Springer-Verlag, Berlin, 1987. MR 932459, DOI 10.1007/BFb0007371
- Stephen Parrott, On a quotient norm and the Sz.-Nagy - Foiaş lifting theorem, J. Functional Analysis 30 (1978), no. 3, 311–328. MR 518338, DOI 10.1016/0022-1236(78)90060-5
- Béla Sz.-Nagy and Ciprian Foiaş, Harmonic analysis of operators on Hilbert space, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York; Akadémiai Kiadó, Budapest, 1970. Translated from the French and revised. MR 0275190
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 777-784
- MSC: Primary 47A20; Secondary 47B35
- DOI: https://doi.org/10.1090/S0002-9939-1989-0972228-9
- MathSciNet review: 972228