A generalization of the Fredholm theorems (Q1910996)
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scientific article; zbMATH DE number 859621
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A generalization of the Fredholm theorems |
scientific article; zbMATH DE number 859621 |
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A generalization of the Fredholm theorems (English)
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24 March 1996
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The present paper deals with some class of bounded operators with closed image in a Banach space with basis. The matrix of an operator of this class resembles an upper triangular matrix in some basis. For example, the classical Fredholm operators belong to this class. It is shown that if the kernel of such an operator \(A\) is trivial, then the equation \(AX= B\) has a solution for any \(B\), that is, a half of the Fredholm alternative can be applied. Some other properties of such operators are also described.
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bounded operators with closed image in a Banach space with basis
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upper triangular matrix
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classical Fredholm operators
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kernel
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Fredholm alternative
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