Riesz Theory Without Axiom of Choice
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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.
compact linear operator, an elementary proof is given for the fourth Riesz theorem where the axiom of choice is avoided, Fredholm operator with index zero, Axiom of choice and related propositions, Riesz theory, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
compact linear operator, an elementary proof is given for the fourth Riesz theorem where the axiom of choice is avoided, Fredholm operator with index zero, Axiom of choice and related propositions, Riesz theory, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
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