A Note on Noncommutative Interpolation
Canadian mathematical bulletin, Tome 46 (2003) no. 1, pp. 59-70

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2003-006-4
Mots-clés : 47A57, 47A20
Constantinescu, T.; Johnson, J. L. A Note on Noncommutative Interpolation. Canadian mathematical bulletin, Tome 46 (2003) no. 1, pp. 59-70. doi: 10.4153/CMB-2003-006-4
@article{10_4153_CMB_2003_006_4,
     author = {Constantinescu, T. and Johnson, J. L.},
     title = {A {Note} on {Noncommutative} {Interpolation}},
     journal = {Canadian mathematical bulletin},
     pages = {59--70},
     year = {2003},
     volume = {46},
     number = {1},
     doi = {10.4153/CMB-2003-006-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-006-4/}
}
TY  - JOUR
AU  - Constantinescu, T.
AU  - Johnson, J. L.
TI  - A Note on Noncommutative Interpolation
JO  - Canadian mathematical bulletin
PY  - 2003
SP  - 59
EP  - 70
VL  - 46
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-006-4/
DO  - 10.4153/CMB-2003-006-4
ID  - 10_4153_CMB_2003_006_4
ER  - 
%0 Journal Article
%A Constantinescu, T.
%A Johnson, J. L.
%T A Note on Noncommutative Interpolation
%J Canadian mathematical bulletin
%D 2003
%P 59-70
%V 46
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-006-4/
%R 10.4153/CMB-2003-006-4
%F 10_4153_CMB_2003_006_4

[1] [1] Agler, J. and McCarthy, J. E., Complete Nevanlinna-Pick kernels. J. Funct. Anal. 175 (2000), 111–124. Google Scholar

[2] [2] Arias, A. and Popescu, G., Noncommutative interpolation and Poisson transforms. Israel J. Math. 115 (2000), 205–234. Google Scholar

[3] [3] Arveson, W., Subalgebras of C*-algebras III: Multivariable operator theory. Acta Math. 181 (1998), 476–514. Google Scholar

[4] [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] [5] Constantinescu, T., Schur Parameters, Factorization and Dilation Problems. Birkhäuser, 1996. Google Scholar

[6] [6] Constantinescu, T. and Johnson, J. L., Tensor algebras and displacement structure I. The Schur algorithm. Preprint, 2001. Google Scholar

[7] [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] [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] [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] [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] [11] Kailath, T. and Sayed, A. H., Displacement structure: theory and applications. SIAM Rev. 37 (1995), 297–386. Google Scholar

[12] [12] Parthasarathy, K. R., An Introduction to Quantum Stochastic Calculus. Birkhäuser, 1992. Google Scholar

[13] [13] Popescu, G., Interpolation problems in several variables. J. Math. Anal. Appl. 227 (1998), 227–250. Google Scholar

[14] [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

Cité par Sources :