  It is a translation of an old paper of mine. We describe the topology tau_p
in the space Pi_p(Y,X), for which the closures of convex sets in tau_p and in
*-weak topology of the space Pi_p(Y,X) are coincident. Thereafter, we
investigate some properties of the space Pi_p, related to this new topology.
2010-remark: Occasionally, the topology is coincides with the lambda_p-topology
from the paper "Compact operators which factor through subspaces of l_p", Math.
Nachr. 281(2008), 412-423 by Deba Prasad Sinha and Anil Kumar Karn.
