Reinov O.I.
 On factorization of operators through the spaces  l^p.

 Abstract:
	 We give conditions on a pair of Banach spaces
	 X and  Y,  under which
	   (*) each operator from  X to  Y, whose second adjoint
	 factors compactly through the space  l^p,
	 1\le p\le+\infty, itself compactly factors through  l^p.
	   The conditions are as follows:
	 either the space  X*, or the space  Y*** possesses
	 the Grothendieck approximation property.
	 The corresponding question for parameters  p>1, p\neq 2,
	 still being open, we show that for  p=1
	 the conditions are essential:
	 there exist Banach spaces with the bases for which
	 the assertion (*) invalid for the case of  l^1-factoring
	 operators.

 2. AMS Subject Classification:  47B10. Hilbert--Schmidt operators,
   trace class operators, nuclear operators, p-summing operators, etc.

 E-mail: orein@orein.usr.pu.ru

 Comments: TeX: AMSTeX. Russian (8 pp.)