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

Kania, Tomasz and Laustsen, Niels Jakob and Skillicorn, Richard (2016) A singular, admissible extension which splits algebraically, but not strongly, of the algebra of bounded operators on a Banach space. Journal of Functional Analysis, 271. pp. 2888-2898. ISSN 0022-1236

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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).

Item Type:
Journal Article
Journal or Publication Title:
Journal of Functional Analysis
Additional Information:
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
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2603
Subjects:
ID Code:
79949
Deposited By:
Deposited On:
07 Jun 2016 10:36
Refereed?:
Yes
Published?:
Published
Last Modified:
26 Nov 2020 03:59