The topology of pointwise, compact and weakly compact convergence on \(\mathcal B(X,Y)\) (Q976556)

Denote by \({\mathcal B}(X,Y)\) the space of bounded linear operators between the Banach spaces \(X\) and \(Y\). In this space, we can consider the following classical topologies: the topology of pointwise, compact and weakly compact convergence on \({\mathcal B}(X,Y)\). The paper under review provides some characterizations of each one of these topologies via the classical operator norm topology on \({\mathcal B}(X,Y)\). In order to do this, the author uses some convenient vector spaces of finite rank operators between \(X\) and \(Y\).