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A simple proof of the Fredholm alternative and a characterization of the Fredholm operators. (English) Zbl 1036.47005

The paper contains simple proofs of the following standard facts: the Fredholm alternative for Fredholm operators (\(\Phi\)-operators with zero index); the coincidence of the set of all Fredholm operators with the set of operators of the form \(B+F\), where \(B\) is invertible and \(F\) has finite rank.

MSC:

47A53 (Semi-) Fredholm operators; index theories
47A50 Equations and inequalities involving linear operators, with vector unknowns
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