## Abstract

This paper introduces a new class (denoted by EK) of operators acting on a direct sum of m copies of ℓ^{2}. Inversion and Fredholm properties of operators in EK are studied. The class EK includes block Toeplitz operators with a rational matrix symbol and non-Toeplitz operators like operators defined by infinite block band matrices. Operators in EK are characterized by the following two properties: (1) the entries a_{jk} in their canonical block matrix representation decay exponentially as functions of |j-k|, and (2) the Kronecker rank is finite. The main tool in the analysis is based on the fact that operators in the class EK can be represented as input-output operators of certain finite dimensional linear time-variant input-output systems. In the description and the study of these systems dichotomy of difference equations plays an important role.

Original language | English |
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Pages (from-to) | 30-77 |

Number of pages | 48 |

Journal | Integral Equations and Operator Theory |

Volume | 18 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1994 |

## Keywords

- AMS classification: Primary 47A53, 93A25, Secondary 93B15, 39A11