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On the Poles of the Local Resolvent
Author(s) -
Bermúdez Teresa,
González Manuel,
Martinón Antonio
Publication year - 1998
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19981930103
Subject(s) - mathematics , resolvent , laurent series , resolvent formalism , banach space , pure mathematics , operator (biology) , gravitational singularity , point (geometry) , function (biology) , chain (unit) , series (stratigraphy) , sequence (biology) , mathematical analysis , finite rank operator , geometry , paleontology , biochemistry , chemistry , physics , repressor , astronomy , evolutionary biology , biology , transcription factor , gene , genetics
We give two characterizations of the isolated singularities of the local resolvent function of an operator T ε L(X) at a point ε of a complex Banach space X : in terms of a suitable decomposition of ε, 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 ε and show that T is chain‐finite if and only if T is locally chain‐finite at every χ ε X.