Injective Tauberian Operators on L1 and Operators with Dense Range on l∞
Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 276-280
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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 ${{\ell }_{\infty }}$ .
Johnson, William; Nasseri, Amir Bahman; Schechtman, Gideon; Tkocz, Tomasz. Injective Tauberian Operators on L1 and Operators with Dense Range on l∞. Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 276-280. doi: 10.4153/CMB-2014-054-5
@article{10_4153_CMB_2014_054_5,
author = {Johnson, William and Nasseri, Amir Bahman and Schechtman, Gideon and Tkocz, Tomasz},
title = {Injective {Tauberian} {Operators} on {L1} and {Operators} with {Dense} {Range} on l\ensuremath{\infty}},
journal = {Canadian mathematical bulletin},
pages = {276--280},
year = {2015},
volume = {58},
number = {2},
doi = {10.4153/CMB-2014-054-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-054-5/}
}
TY - JOUR AU - Johnson, William AU - Nasseri, Amir Bahman AU - Schechtman, Gideon AU - Tkocz, Tomasz TI - Injective Tauberian Operators on L1 and Operators with Dense Range on l∞ JO - Canadian mathematical bulletin PY - 2015 SP - 276 EP - 280 VL - 58 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-054-5/ DO - 10.4153/CMB-2014-054-5 ID - 10_4153_CMB_2014_054_5 ER -
%0 Journal Article %A Johnson, William %A Nasseri, Amir Bahman %A Schechtman, Gideon %A Tkocz, Tomasz %T Injective Tauberian Operators on L1 and Operators with Dense Range on l∞ %J Canadian mathematical bulletin %D 2015 %P 276-280 %V 58 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-054-5/ %R 10.4153/CMB-2014-054-5 %F 10_4153_CMB_2014_054_5
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