In Gohberg et al. (Classes of linear operators, Theorem 4.2, Chapter XVII. Birkhäuser, Basel, 2003), some sufficient conditions are given so that if A is an unbounded Fredholm linear operator and if B is another (possibly unbounded) linear operator, then their algebraic sum A + B is a Fredholm operator. The main objective here consists of extending the previous result to the case of three unbounded linear operators. Namely, some sufficient conditions are given so that if A, B, C are three unbounded linear operators with A being a Fredholm operator, then their algebraic sum A + B + C is also a Fredholm operator.
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