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On the existence of a fixed point of the operator acting in the space of continuous functions

✍ Scribed by A. Pokrovskii; D. Rachinskii


Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
167 KB
Volume
20
Category
Article
ISSN
0362-546X

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Every non-reflexive subspace of K(H), the space of compact operators on a Hilbert space H, contains an asymptotically isometric copy of c 0 . This, along with a result of Besbes, shows that a subspace of K(H) has the fixed point property if and only if it is reflexive.

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## Abstract The purpose of this paper is to study the existence of fixed points for the sum of two nonlinear operators in the framework of real Banach spaces. Later on, we give some examples of applications of this type of results (Β© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)