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1. CMB 2014 (vol 58 pp. 276)

Johnson, William; Nasseri, Amir Bahman; Schechtman, Gideon; Tkocz, Tomasz
 Injective Tauberian Operators on $L_1$ and Operators with Dense Range on $\ell_\infty$ There exist injective Tauberian operators on $L_1(0,1)$ that have dense, nonclosed range. This gives injective, nonsurjective operators on $\ell_\infty$ that have dense range. Consequently, there are two quasi-complementary, noncomplementary subspaces of $\ell_\infty$ that are isometric to $\ell_\infty$. Keywords:$L_1$, Tauberian operator, $\ell_\infty$Categories:46E30, 46B08, 47A53
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