Injective Tauberian operators on $L_1$ and operators with dense range on ${\ell }_{\infty }$

William B. Johnson, Amir Bahman Nasseri, Gideon Schechtman +1

There exist injective Tauberian operators on $L_1(0,1)$ that have dense, non closed range. This gives injective, non surjective operators on ${\ell }_{\infty }$ that have dense range. Co…