Browsing by Subject "Ideal"

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    On S₁-strictly singular operators
    (2010-05) Teixeira, Ricardo Verotti O.; Odell, E. (Edward); Todd, Arbogast; Treisman, Philip U.; Vishik, Mikhail; Schlumprecht, Thomas
    Let X be a Banach space and denote by SS₁(X) the set of all S₁-strictly singular operators from X to X. We prove that there is a Banach space X such that SS₁(X) is not a closed ideal. More specifically, we construct space X and operators T₁ and T₂ in SS₁(X) such that T₁+T₂ is not in SS₁(X). We show one example where the space X is reflexive and other where it is c₀-saturated. We also develop some results about S_alpha-strictly singular operators for alpha less than omega_1.