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( 0, 1 ) that have dense, nonclosed range. This gives injective nonsurjective operators on _∞ that have dense range. Consequently, there are two quasi-complementary noncomplementary subspaces of _∞ that are isometric to _∞ .