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Local Contractions of Banach Spaces and Spectral Gap Conditions

✍ Scribed by Mohamed S. ElBialy

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
251 KB
Volume
182
Category
Article
ISSN
0022-1236

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✦ Synopsis

We study the linearization problem for a C k, 1 , k 1, contraction of a Banach space E near a fixed point which satisfies a spectral gap condition and a narrow band condition both of order k. We also assume that the part of the spectrum in each band satisfies a finite non-resonant condition of order k relative to itself together with the part that lies in the larger bands. We show that there is a C k, ; linearization for sufficiently small ;>0. We give a precise estimate on ; in terms of the gap and band conditions.

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