Kania, Tomasz, 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 (10). pp. 2888-2898. doi:10.1016/j.jfa.2016.05.019 ISSN 0022-1236.

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Abstract

Let E be the Banach space constructed by Read [10] 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 [1], and complements recent results of Laustsen and Skillicorn [6].

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Linear operators, Banach spaces, Banach algebras
Journal or Publication Title:	Journal of Functional Analysis
Publisher:	Academic Press
ISSN:	0022-1236
Official Date:	15 November 2016
Dates:	Date Event 15 November 2016 Published 2 June 2016 Available 26 May 2016 Accepted 17 March 2016 Submitted
Volume:	271
Number:	10
Page Range:	pp. 2888-2898
DOI:	10.1016/j.jfa.2016.05.019
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	12 August 2016
Date of first compliant Open Access:	2 June 2017
Funder:	European Research Council (ERC)
Grant number:	Grant Agreement no. 291497

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