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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Riesz theory without axiom of choice


Author: Erich Martensen
Journal: Proc. Amer. Math. Soc. 99 (1987), 496-500
MSC: Primary 47B05; Secondary 04A25
DOI: https://doi.org/10.1090/S0002-9939-1987-0875387-X
MathSciNet review: 875387
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Abstract: 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$ 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.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0875387-X
Article copyright: © Copyright 1987 American Mathematical Society