A singular, admissible extension which splits algebraically, but not strongly, of the algebra of bounded operators on a Banach space

Niels Jakob Laustsen; Richard Skillicorn; Tomasz Kania

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A singular, admissible extension which splits algebraically, but not strongly, of the algebra of bounded operators on a Banach space

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arxiv 1603.04275 v1 pith:BNNCMQGG submitted 2016-03-14 math.FA math.KTmath.RA

Tomasz Kania , Niels Jakob Laustsen , Richard Skillicorn This is my paper · ORCID

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abstract

Let $E$ be the Banach space constructed by Read (J. London Math. Soc. 1989) such that the Banach algebra $\mathscr{B}(E)$ of bounded operators on $E$ admits a discontinuous derivation. We show that $\mathscr{B}(E)$ 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 (Mem. Amer. Math. Soc. 1999), and complements recent results of Laustsen and Skillicorn (C. R. Math. Acad. Sci. Paris, to appear).

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