Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2008; 45(1): 151-161

Printed January 1, 2008

Copyright © The Korean Mathematical Society.

Fixed points, eigenvalues and surjectivity

In-Sook Kim

Sungkyunkwan University

Abstract

We prove that a countably condensing operator defined on a closed wedge in a Banach space has a fixed point if it is strictly quasibounded, by using an index theory for such operators. From this, the existence of eigenvalues and surjectivity are deduced.

Keywords: fixed points, eigenvalues, surjectivity, countably condensing maps

MSC numbers: 47H10, 47J10, 47H09