## 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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