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中文摘要：
设X,Y为Banach空间，T为从X到Y的线性算子．T的值域R（T）≠Y且为逼近紧子空间，T的零空间N（T）≠{θ}．证得不适定算子方程Tx=y的最佳逼近解对任意y∈Y均存在的充分必要条件是N（T）为X的迫近子空间．
英文摘要：
Let X,Y be Banach space, T be linear operator from X to Y. The range of T, R （T） ≠ Y and R（T） is approximation compact sub-space. The null space of T,N（T） ≠ {θ}. We prove that the best approximation solution of ill-posed operator equation Tx = y exists for every y ∈ Y if and only if N（T） is approximation sub-space of X.
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