Spaces of diagonal operators (Q5947794)

The author studies the structure of spaces of operators on a Banach space that are diagonal with respect to a given basis. In particular, the question of when the space of compact diagonal operators has a subspace isomorphic to \(c_0\) is treated in detail, with a necessary and a sufficient condition that this be so proved. Using these results, the author gives examples of reflexive Banach spaces with bases for which \(c_0\) cannot be embedded in the space of compact diagonal maps. The work is motivated by previous results of Sersouri, Emmanuele, and Feder of an analogous nature.