[Author]
 O. I. Reinov

[Title]
 Approximation of operators in Banach spaces

[AMS Subj-class]
 46B28 Spaces of operators; tensor products; approximation properties

[Abstract]
 It is a translation of an old paper of the author.
 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.


[Comments]
 AMSTeX, English, 10 pp.
 Just a translation of an old paper of the author ("Approximation of operators
 in Banach spaces", in the collection "Primenenie funkcional'nogo analiza v 
 teorii priblizhenij" (1985), 128-142), with nonessential changes and remarks. 
 Two aims: the paper is difficult to get even in Russian, and it is to apply 
 its main results in a next preprint to answer an open question posed in a 
 Math. Nachr. paper of 2008.

[Contact e-mail]
 orein51@mail.ru