Splittings of extensions and homological bidimension of the algebra of bounded operators on a Banach space

Laustsen, Niels Jakob and Skillicorn, Richard (2016) Splittings of extensions and homological bidimension of the algebra of bounded operators on a Banach space. Comptes Rendus Mathématique, 354 (5). pp. 459-463. ISSN 1631-073X

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Abstract

We show that there exists a Banach space E such that: - the Banach algebra B(E) of bounded, linear operators on E has a singular extension which splits algebraically, but it does not split strongly; - the homological bidimension of B(E) is at least two. The first of these conclusions solves a natural problem left open by Bade, Dales, and Lykova (Mem. Amer. Math. Soc. 1999), while the second answers a question of Helemskii. The Banach space E that we use was originally introduced by Read (J. London Math. Soc. 1989).

Item Type:

Journal Article

Journal or Publication Title:

Comptes Rendus Mathématique

Additional Information:

This is the author’s version of a work that was accepted for publication in Comptes Rendus Mathematique. 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 Comptes Rendus Mathematique, 354, 5, 2016 DOI: 10.1016/j.crma.2015.12.020

Uncontrolled Keywords:

/dk/atira/pure/subjectarea/asjc/2600/2600

Subjects:

?? bounded, linear operatorbanach spacebanach algebrashort-exact sequencealgebraic splittingstrong splittingsingular extensionadmissible extensionpullbacksecond continuous hochschild cohomology grouphomological bidimensiongeneral mathematicsmathematics(all) ??

Departments:

Faculty of Science and Technology > Mathematics and Statistics

ID Code:

78198

Deposited By:

ep_importer_pure

Deposited On:

04 Apr 2016 10:22

Refereed?:

Yes

Published?:

Published

Last Modified:

23 Jun 2025 00:28

URI:

https://eprints.lancs.ac.uk/id/eprint/78198