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Injective Tauberian Operators on L1 and Operators with Dense Range on ℓ∞

Published online by Cambridge University Press:  20 November 2018

William Johnson ,
Amir Bahman Nasseri ,
Gideon Schechtman  and
Tomasz Tkocz
William Johnson
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA. e-mail: johnson@math.tamu.edu
Amir Bahman Nasseri
Affiliation:
Fakultät für Mathematik, Technische Universität Dortmund, D-44221 Dortmund, Germany. e-mail: amirbahman@hotmail.de
Gideon Schechtman
Affiliation:
Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel. e-mail: gideon@weizmann.ac.il
Tomasz Tkocz
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK. e-mail: t.tkocz@warwick.ac.uk
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Abstract.

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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 ${{\ell }_{\infty }}$.

Keywords

46E3046B0847A53L1Tauberian operatorℓ∞
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 2 , 01 June 2015 , pp. 276 - 280
Copyright
Copyright © Canadian Mathematical Society 2015

References

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