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
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