Riesz theory without axiom of choice
Erich Martensen · Proceedings of the American Mathematical Society · 1987
In this paper the Riesz theory for compact linear operators in a normed vector space is considered from the point of view of how far the axiom of choice is involved. Special attention is drawn to the theorem, by which for the operator I − A , A I - A,A being compact, the index vanishes and the nullspace has a closed algebraic complement. It is shown that this can be proved without making use of the axiom of choice.