Injective Tauberian Operators on L1 and Operators with Dense Range on ℓ∞

Abstract

Abstract.There exist injective Tauberian operators on L1(0, 1) that have dense, nonclosed range. This gives injective nonsurjective operators on ℓ∞ that have dense range. Consequently, there are two quasi-complementary noncomplementary subspaces of ℓ∞ that are isometric to ℓ∞.