[Author]
O. I. Reinov
[Title]
Approximation properties and some classes of operators
[AMS Subj-class]
47B10 Hilbert--Schmidt operators, trace class operators,
nuclear operators, p-summing operators, etc.
[Abstract]
Among others, we consider in detail some questions around
the properties of operators with $p$-nuclear adjoints.
For $p=1,\infty$, we give also new examples of operators,
which can not be factored through $L_p$-spaces, but
whose adjoints factor compactly through $l_{p'}$-spaces.
We show that, for any $p\in[1,\infty]$, all Banach spaces
have the (new) so called approximation property $AP(l_p)$,
connected with the compact factorizatons of operators
through $l_p$, if and only if every operator, whose
adjoint factors compacly through $l_{p'}$, can be factored
(compactly) through the space $l_p$.
[Comments]
AmSTeX, 60 pp., Russian
[Contact e-mail]
orein@orein.usr.pu.ru