Uniform factorization for p-compact sets of p-compact linear operators

Obtaining a factorization of p-compact linear operators via universal Banach spaces, and using the lifting property of quotient maps for p-compact sets we prove a factorization result for relatively r-compact subsets of p  -compact operators, where r≥2r≥2, 1≤p≤r<∞1≤p≤r<∞. To apply our results to homogeneous polynomials, in particular, we show that relatively p-compact subsets of a Banach space of p-compact operators are collectively p-compact.