Smooth points and M-ideals (Q2367768)

The authors characterize the smooth points of the unit ball of \({\mathcal L} (\ell^ p, E)\), where \(1<p <\infty\) and \(E\) is an arbitrary Banach space, under the assumption that \({\mathcal H} (\ell^ p, E)\) is an \(M\)- ideal in \({\mathcal L} (\ell^ p, E)\). In particular, they obtain the description of the smooth points of the unit ball of \({\mathcal L} (\ell^ p, \ell^ r)\) for \(p,r\in (1,\infty)\).