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On the Poles of the Local Resolvent

✍ Scribed by Teresa Bermúdez; Manuel González; Antonio Martinón

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
382 KB
Volume
193
Category
Article
ISSN
0025-584X

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✦ Synopsis

We give two characterizations of the isolated singularities of the local resolvent function of an operator T E L ( X ) at a point z of a complex Banach space X: in terms of a suitable decomposition of x, and in terms of the existence of a sequence in X related with the Laurent series of the local resolvent function. Moreover, we introduce the locally chain-finite operators at a point x E X and show that T is chain-finite if and only if T is locally chain-finite at every x E X.

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