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Extensions and the weak Calkin algebra of Read's Banach space admitting discontinuous derivations

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>10/11/2016
<mark>Journal</mark>Studia Mathematica
Volume236
Number of pages12
Pages (from-to)51-62
Publication StatusPublished
<mark>Original language</mark>English

Abstract

Read produced the first example of a Banach space E such that the associated Banach algebra B(E) of bounded operators admits a discontinuous derivation (J. London Math. Soc. 1989). We generalize Read's main theorem about B(E) from which he deduced this conclusion, as well as the key technical lemmas that his proof relied on, by constructing a strongly split-exact sequence
{0}→W(E)→B(E)→l2~→{0},
W(E) where W(E) denotes the ideal of weakly compact operators on E, while l2~ is the unitization of the Hilbert space l2, endowed with the zero product.