Riesz theory without axiom of choice
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- by Erich Martensen PDF
- Proc. Amer. Math. Soc. 99 (1987), 496-500 Request permission
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.References
- David L. Colton and Rainer Kress, Integral equation methods in scattering theory, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1983. A Wiley-Interscience Publication. MR 700400
- Harro Heuser, Funktionalanalysis, Mathematische Leitfäden, B. G. Teubner, Stuttgart, 1975 (German). MR 0482021
- Friedrich Riesz, Über lineare Funktionalgleichungen, Acta Math. 41 (1916), no. 1, 71–98 (German). MR 1555146, DOI 10.1007/BF02422940
Additional Information
- © Copyright 1987 American Mathematical Society
- 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