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Some characterization of Atkinson & Fredholm operators
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In this paper, we study the Atkinson operator and Fredholm operator. We showed that every Atkinson operator with a nonpositive index could be represented as a finite-dimensional perturbation of a left-invertible Atkinson operator. Similar theorems can then be proved for Atkinson operators with non-negative index and Fredholm operators with zero and arbitrary index. With the help of these theorems, we gave a unique characterization of the index except for a rational factor.
Title: Some characterization of Atkinson & Fredholm operators
Description:
In this paper, we study the Atkinson operator and Fredholm operator.
We showed that every Atkinson operator with a nonpositive index could be represented as a finite-dimensional perturbation of a left-invertible Atkinson operator.
Similar theorems can then be proved for Atkinson operators with non-negative index and Fredholm operators with zero and arbitrary index.
With the help of these theorems, we gave a unique characterization of the index except for a rational factor.
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