f(x-y)dy, where β ≥ n and ρ is a norm function which is homogeneous with respect to certain nonistropic dialation.
Fm is said to be separable if a = h k for some h ∈ Fn, k ∈ Fm. A linear orperator A on Fn Fm is said to be strongly separable if x ∈ Fn Fm is separable if and only if Ax is separable. It is proved that a linear operator A on Fn Fn is strongly separable if and only if A = A1 A2 or A = A1 T A2 for some linear bijections A1,A2 on Fn. Next, it is shown that when m ≠ n, a linear operator A on Fn Fm is strongly separable if and only if A = A1 A2 for some linear bijections A1,A2 on Fn, Fm, respectively. Lastly, relationships among separable operators, strongly separable operators and rank-1 preservers are discussed.
