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

Ramm, A. G.

Am. Math. Mon. 108, No. 9, 855-860 (2001).

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.

Reviewer: Vladimir S. Pilidi (Rostov-na-Donu)

MSC:

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

Keywords:

Fredholm operator; Fredholm alternative; operator equation; finite-rank operator