J. Korean Math. Soc. 2005; 42(6): 1205-1213
Printed November 1, 2005
Copyright © The Korean Mathematical Society.
In-Sook Kim
Sungkyunkwan University
Applying a fixed point theorem for compact admissible maps due to G\'orniewicz, we prove that under certain conditions each countably condensing admissible maps in Fr\'echet spaces has a positive eigenvalue. This result has many consequences, including the well-known theorem of Krasnoselskii.
Keywords: eigenvalues, countably condensing maps, admissible maps, measures of noncompactness
MSC numbers: 47J10, 47H09, 54C60
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