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

Laustsen, Niels Jakob and Skillicorn, Richard (2016) Extensions and the weak Calkin algebra of Read's Banach space admitting discontinuous derivations. Studia Mathematica, 236. pp. 51-62. ISSN 0039-3223

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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.

Item Type:
Journal Article
Journal or Publication Title:
Studia Mathematica
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
81441
Deposited By:
Deposited On:
14 Sep 2016 09:14
Refereed?:
Yes
Published?:
Published
Last Modified:
09 Aug 2020 04:35