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  • KaniaLaustsenSkillicorn

    Rights statement: This is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, 271, 2016 DOI: 10.1016/j.jfa.2016.05.019

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A singular, admissible extension which splits algebraically, but not strongly, of the algebra of bounded operators on a Banach space

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published
<mark>Journal publication date</mark>20/09/2016
<mark>Journal</mark>Journal of Functional Analysis
Volume271
Number of pages11
Pages (from-to)2888-2898
Publication StatusPublished
Early online date2/06/16
<mark>Original language</mark>English

Abstract

Let E be the Banach space constructed by Read (J. London Math. Soc. 1989) such that the Banach algebra B(E) of bounded operators on E admits a discontinuous derivation. We show that B(E) has a singular, admissible extension which splits algebraically, but does not split strongly. This answers a
natural question going back to the work of Bade, Dales, and Lykova (Mem. Amer. Math. Soc. 1999), and complements recent results of Laustsen and Skillicorn (C.R. Math. Acad. Sci. Paris 2016).

Bibliographic note

This is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, 271, 2016 DOI: 10.1016/j.jfa.2016.05.019