[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