Pure Mathematics Seminar: Richard Skillicorn
Richard Skillicorn, Lancaster University
Wednesday 30 April 2014, 1500-1600
A54, Postgraduate Statistics Centre Lecture Theatre
Extensions of Banach Algebras: Algebraic and Strong Splittings
An extension 0 --> I --> B --> A --> 0 of a Banach algebra A splits algebraically if there is an algebra homomorphism rho: A--> B which is a right inverse of pi: B-->A, and splits strongly if rho is also continuous.
Bade, Dales and Lykova (1999) studied which Banach algebras A have the property that every extension which splits algebraically automatically splits strongly. For the case A=B(E), the Banach algebra of bounded operators on a Banach space E, they observed that no extension which splits algebraically, but not strongly, is known; their question was whether this is true in general.
We answer this question in the negative, using a Banach space constructed by Read (1989).