[Banach] Abstract of a paper by William B. Johnson, Amir Bahman Nasseri, Gideon Schechtman and Tomasz Tkocz

This is an announcement for the paper "Injective Tauberian operators on $L_1$ and operators with dense range on $\ell_\infty$" by William B. Johnson, Amir Bahman Nasseri, Gideon Schechtman and Tomasz Tkocz.

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 $\ell_\infty$.

Archive classification: math.FA

Mathematics Subject Classification: 46E30, 46B08, 47A53

Submitted from: gideon@weizmann.ac.il

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1408.1443

or

http://arXiv.org/abs/1408.1443