[Authors] Reinov O. I., Reinov Ju. I. [Title] Approximation properties, $N_p$-operators and $l_p$-operators [AMS Subj-class] 47B10 Hilbert--Schmidt operators, trace class operators, nuclear operators, p-summing operators, etc. [Abstract] Further investigations of approximation properties defined by the ideals of p-nuclear operators and operators which admit factorizations through $L_p$-spaces. [Comments] AMSTeX, Russian, 34 pp. [Contact e-mail] orein51@mail.ru