Injective Tauberian Operators on L1 and Operators with Dense Range on ℓ∞. Issue 2 (1st June 2015)

• Record Type: Journal Article
• Authors: Johnson, William; Bahman Nasseri, Amir; Schechtman, Gideon; Tkocz, Tomasz
• Is Part Of: Canadian mathematical bulletin =. Volume 58:Issue 2(2015)
• Page Start: 276
• Page End: 280
• Publication Date: 2015-06-01
• Subjects: 46E30 -- 46B08 -- 47A53; L1 -- Tauberian operator -- ℓ∞; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2014-054-5
• Languages: English
• ISSNs: 0008-4395

Abstract

Abstract: There exist injective Tauberian operators on ${{L}_{1}}\left( 0, \, 1 \right)$ 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 ${{\ell }_{\infty }}$ .