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Ideal properties of the Dunford integration operator
Author(s) -
Bertoloto F.,
Botelho G.,
Jatobá A.
Publication year - 2015
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.201400181
Subject(s) - mathematics , approximation property , finite rank operator , banach space , strictly singular operator , separable space , ideal (ethics) , compact operator , pure mathematics , c0 semigroup , banach manifold , operator (biology) , lp space , discrete mathematics , operator space , mathematical analysis , extension (predicate logic) , computer science , philosophy , biochemistry , chemistry , epistemology , repressor , transcription factor , gene , programming language
Let F be a Banach space. We establish necessary and sufficient conditions for the Dunford integration operator, from the space of F ‐valued Dunford integrable functions to the bidual F ′ ′of F , to belong to a given operator ideal. We also show how this fact can be used to characterize important classes of Banach spaces, such as Banach spaces with the Banach‐Saks property, separable Banach spaces not containing c 0 , Banach spaces not containing c 0 or ℓ 1 and Asplund spaces not containing c 0 .