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

Abstract

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. Consequently, there are two quasi-complementary, non complementary subspaces of ${\ell }_{\infty }$ that are isometric to ${\ell }_{\infty }$.

References in corpus (1)

• The Spectrum of Operators on C(K) with the Grothendieck Property and Characterization of J-Class Operators which are adjoints