[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