Discontinuous Derivations on the Algebra of Bounded Operators on a Banach Space
C. J. Read · Journal of the London Mathematical Society · 1989
It is a question of general interest whether, on a given Banach algebra A, there is any discontinuous derivation from A into M, where M is a Banach A-bimodule. In the case when A is B(E), the algebra of all bounded operators on a Banach space E, there are a number of known conditions on E which ensure that derivations from B(E) are automatically continuous (for example, if E is isomorphic to its square). Until now, there have been no examples of Banach spaces E such that discontinuous derivations from B(E) are known to exist. In this paper we exhibit a class of Banach spaces E such that discontinuous derivations exist on B(E); in the process, we discover various new Banach spaces which are not isomorphic to their squares.