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中文摘要：
设F是一个域，a∈F^n⊙F^m．若存在h∈F^m，k∈F^m，使得a=h⊙k，则称a是可分的．空间F^n⊙F^m上的线性算子A称为是强可分的，是指∨x∈F^m,x可分→←Ax可分．本文证明了F^n⊙F^n上的线性算子A是强可分的当且仅当存在Fn上的线性双射A1与A2，使得A=A1⊙A2或A=A1⊙TA2；证明了F^n⊙F^m（n≠m）上线性算子A是强可分的当且仅当存在F^n与F^m上的线性双射A1与A2，使得A=A1⊙A2．最后，给出了可分算子、强可分算子和秩1保持映射之间的关系．
英文摘要：
Let F be a field. An element a in F^n⊙F^m is said to be separable if a = h⊙k for some h∈ F^n,k∈F^m.A linear orperator A on F^n⊙ F^m is said to be strongly separable if x∈ F^n ⊙F^m is separable if and only if Ax is separable. It is provedthat a linear operator A on F^n⊙ F^n is strongly separable if and only if A = A1 ⊙ A2or A = A1 ⊙T A2 for some linear bijections A1, A2 on F^n. Next, it is shown that when m≠ n, a linear operator A on F^n ⊙ F^m is strongly separable if and only if A = A1⊙A2for some linear bijections A1, A2 on F^n, F^m, respectively. Lastly, relationships among separable operators, strongly separable operators and rank-1 preservers are discussed.
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