Abstract
LetT be a compact linearK-positive irreducible operator on a Banach spaceY with a coneK and letT h be aK-positive approximation ofT on a subspaceY h ⊂ Y. It is shown that the principal eigenelements ofT h approximate the corresponding eigenelements ofT with the same accuracy as the exact normalized positive eigenvector can be approximated by elements inY h. This result is then extended to eigenvalue problems of the typeMu = λNu with generally unboundedM and compact irreducibleK-positiveT = M −1N.
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Marek, I. Approximations of the principal eigenelements inK-positive non-selfadjoint eigenvalue problems. Math. Systems Theory 5, 204–215 (1971). https://doi.org/10.1007/BF01694177
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DOI: https://doi.org/10.1007/BF01694177