Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9495410 | Journal of Functional Analysis | 2005 | 36 Pages |
Abstract
The Carathéodory problem in the N-variable non-commutative Herglotz-Agler class and the Carathéodory-Fejér problem in the N-variable non-commutative Schur-Agler class are posed. It is shown that the Carathéodory (resp., Carathéodory-Fejér) problem has a solution if and only if the non-commutative polynomial with given operator coefficients (the data of the problem indexed by an admissible set Î) takes operator values with positive semidefinite real part (resp., contractive operator values) on N-tuples of Î-jointly nilpotent contractive nÃn matrices, for all nâN.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Dmitry S. KalyuzhnyıË-VerbovetzkiıË,