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. / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/ETD-UT-2010-05-1205 |
| Date | 08 October 2010 |
| Creators | Teixeira, Ricardo Verotti O. |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Type | thesis |
| Format | application/pdf |
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