Exponentially dominated infinite block matrices of finite Kronecker rank

A. Ben-Artzi, I. Gohberg, M. A. Kaashoek

Research output: Contribution to journalArticlepeer-review

Abstract

This paper introduces a new class (denoted by EK) of operators acting on a direct sum of m copies of ℓ2. 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 ajk 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 languageEnglish
Pages (from-to)30-77
Number of pages48
JournalIntegral Equations and Operator Theory
Volume18
Issue number1
DOIs
StatePublished - Mar 1994

Keywords

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

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