New criteria for a decomposable operator (Q1822328)

The authors give four new necessary and sufficient conditions for a decomposable operator on complex Banach space. The most novel of these criteria, that an operator is decomposable if and only if it and its adjoint both have property (\(\beta)\), generalizes a result of the first author for reflexive spaces. The proof first requires generalizing some duality results of Bishop from the reflexive to the arbitrary case.