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  • CRLaustsenSkillicorn

    Rights statement: 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

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

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>05/2016
<mark>Journal</mark>Comptes Rendus Mathématique
Issue number5
Volume354
Number of pages5
Pages (from-to)459-463
Publication StatusPublished
Early online date24/03/16
<mark>Original language</mark>English

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).

Bibliographic note

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