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Journal of Operator Theory

Volume 67, Issue 1, Winter 2012  pp. 121-152.

Super strictly singular and cosingular operators and related classes

Authors Julio Flores (1), Francisco L. Hernandez (2), Yves Raynaud (3)
Author institution: (1) Departamento de Matematica Aplicada, Universidad Rey Juan Carlos, Mostoles (Madrid), 28933, Spain
(2) Departamento de Analisis Matematico, Universidad Complutense, Madrid, 28940, Spain
(3) Institute de Mathematiques de Jussieu (CNRS-UMR 7586), case 186, UPMC-Universite Paris-06, Paris, 75005, France

Summary:  The notions of super strictly singular and cosingular operators are revisited and new characterizations given in terms of ultrapowers and operator local representability. The behaviour of the associated (Bernstein and Mityagin) $s$-numbers with respect to duality, ultraproducts and local representability is considered. We also give properties of these classes in the Banach lattice setting like a Dodds--Fremlin type domination result and introduce the class of super disjointly stricty singular operators. The equivalence between lattice strictly singular and disjointly strictly singular operators is considered, and we show that at the super level both classes coincide.

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