On S₁-strictly singular operators
| Title: | On S₁-strictly singular operators |
| Author: | Teixeira, Ricardo Verotti O. |
| Abstract: | 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. |
| Subject: |
Strictly singular operator
Ideal Banach space Functional analysis Schreier sets Rosenthal's theorem |
| URI: | http://hdl.handle.net/2152/ETD-UT-2010-05-1205 |
| Date: | 2010-05 |
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