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Characterizations of strictly singular operators on Banach lattices
Author(s) -
Flores J.,
Hernández F. L.,
Kalton N. J.,
Tradacete P.
Publication year - 2009
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdp007
Subject(s) - mathematics , strictly singular operator , equivalence (formal languages) , pure mathematics , operator (biology) , banach space , singular solution , order (exchange) , discrete mathematics , mathematical analysis , finite rank operator , quasinormal operator , biochemistry , chemistry , finance , repressor , transcription factor , economics , gene
New characterizations of strictly singular operators between Banach lattices are given. It is proved that, for Banach lattices X and Y such that X has finite cotype and Y satisfies a lower 2‐estimate, an operator T : X → Y is strictly singular if and only if it is disjointly strictly singular and ℓ 2 ‐singular. Moreover, if T is regular then the same equivalence holds provided that Y is just order continuous. Furthermore, it is shown that these results fail if the conditions on the lattices are relaxed.