Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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EIGENVALUES OF COUNTABLY CONDENSING MAPS

  • Kim, In-Sook (DEPARTMENT OF MATHEMATICS SUNGKYUNKWAN UNIVERSITY) ;
  • Kim, Yun-Ho (DEPARTMENT OF MATHEMATICS SUNGKYUNKWAN UNIVERSITY) ;
  • Kwon, Sung-Hui (DEPARTMENT OF MATHEMATICS SUNGKYUNKWAN UNIVERSITY)
  • Published : 2009.03.31
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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 haracteristic, that is, the infimum of all $k\;{\geq}\;1$ for which there is a countably k-set-contractive retraction of the closed unit ball of X onto its boundary.

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References

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