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In this paper, we characterize compact linear operators from Banach function spaces to Banach spaces by means of approximations with bounded homogeneous maps. To do so, we undertake a detailed study of such maps, proving a factorization theorem and paying special attention to the equivalent strong domination property involved. Some applications to compact maximal extensions of operators are also given.

Factorization Theorems for Homogeneous Maps on Banach Function Spaces and Approximation of Compact Operators