Injective Tauberian Operators on L1 and Operators with Dense Range on ℓ∞. Issue 2 (1st June 2015) - Johnson, William; Bahman Nasseri, Amir; Schechtman, Gideon; Tkocz, Tomasz
Abstract: There exist injective Tauberian operators on ${L_{1}}\left( 0, \, 1 \right)$ that have dense, nonclosed range. This gives injective nonsurjective operators on ${{\ell }_{∞ }}$ that have dense range. Consequently, there are two quasi-complementary noncomplementary subspaces of ${{\ell }_{∞ }}$ that are isometric to ${{\ell }_{∞ }}$ .