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A Note on Noncommutative Interpolation

Published online by Cambridge University Press:  20 November 2018

T. Constantinescu  and
J. L. Johnson
T. Constantinescu
Affiliation:
Department of Mathematics, University of Texas at Dallas, Box 830688, Richardson, TX 75083-0688, USA, email: [email protected]@utdallas.edu
J. L. Johnson
Affiliation:
Department of Mathematics, University of Texas at Dallas, Box 830688, Richardson, TX 75083-0688, USA, email: [email protected]@utdallas.edu
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Abstract

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In this paper we formulate and solve Nevanlinna-Pick and Carathéodory type problems for tensor algebras with data given on the $N$-dimensional operator unit ball of a Hilbert space. We develop an approach based on the displacement structure theory.

Keywords

47A5747A20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 1 , 01 March 2003 , pp. 59 - 70
Copyright
Copyright © Canadian Mathematical Society 2003

References

[1] Agler, J. and McCarthy, J. E., Complete Nevanlinna-Pick kernels. J. Funct. Anal. 175 (2000), 111–124.Google Scholar
[2] Arias, A. and Popescu, G., Noncommutative interpolation and Poisson transforms. Israel J. Math. 115 (2000), 205–234.Google Scholar
[3] Arveson, W., Subalgebras of C*-algebras III: Multivariable operator theory. Acta Math. 181 (1998), 476–514.Google Scholar
[4] Ball, J. A., Gohberg, I. and Kaashoek, M. A., Nevanlinna-Pick interpolation problem for time-varying input-output maps: The discrete case. In: Operator Theory: Advances and Applications, Vol. 56, Birkhäuser, 1992, 1–51.Google Scholar
[5] Constantinescu, T., Schur Parameters, Factorization and Dilation Problems. Birkhäuser, 1996.Google Scholar
[6] Constantinescu, T. and Johnson, J. L., Tensor algebras and displacement structure I. The Schur algorithm. Preprint, 2001.Google Scholar
[7] Constantinescu, T., Sayed, A. H. and Kailath, T., Inverse scattering experiments, structured matrix inequalities, and tensor algebras. Linear Alg. Appl., to appear.Google Scholar
[8] Davidson, K. R. and Pitts, D. R., The algebraic structure of non-commutative analytic Toeplitz algebras. Math. Ann. 311 (1998), 275–303.Google Scholar
[9] Davidson, K. R. and Pitts, D. R., Nevanlinna-Pick interpolation for noncommutative analytic Toeplitz algebras. Integral Equations Operator Theory 31 (1998), 321–337.Google Scholar
[10] Dewilde, P. and Dym, H., Interpolation for upper triangular operators. In: Operator Theory: Advances and Applications, Vol. 56, Birkhäuser, 1992, 153–260.Google Scholar
[11] Kailath, T. and Sayed, A. H., Displacement structure: theory and applications. SIAM Rev. 37 (1995), 297–386.Google Scholar
[12] Parthasarathy, K. R., An Introduction to Quantum Stochastic Calculus. Birkhäuser, 1992.Google Scholar
[13] Popescu, G., Interpolation problems in several variables. J. Math. Anal. Appl. 227 (1998), 227–250.Google Scholar
[14] Sayed, A. H., Constantinescu, T. and Kailath, T., Lattice structures for time variant interpolation problems. In: Proc. IEEE Conf. Decision and Contr., Vol. 1, Tucson, 1992, 116–121.Google Scholar