Characterizations of strictly singular operators on Banach lattices

J. Flores; F. L. Hernández; N. J. Kalton; P. Tradacete
June 2009
Journal of the London Mathematical Society;Jun2009, Vol. 79 Issue 3, p612
Academic Journal
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 ℓ2-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.


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