Eigenvalues of countably condensing maps
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Using an index theory for countably condensing maps, we show the existence of eigenvalues for countably k-set contractive maps and countably condensing maps in an infinite dimensional Banach space X, under certain condition that depends on the quantitative characteristic, that is, the infimum of all k≥ 1 for which there is a countably k-set-contractive retraction of the closed unit ball of X onto its boundary.
Abstract
Using an index theory for countably condensing maps, we show the existence of eigenvalues for countably k-set contractive maps and countably condensing maps in an infinite dimensional Banach space X, under certain condition that depends on the quantitative characteristic, that is, the infimum of all k≥ 1 for which there is a countably k-set-contractive retraction of the closed unit ball of X onto its boundary.
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