Abstract
We prove that a Banach space X has the bounded approximation property if and only if, for every separable Banach space Z and every injective operator T from Z to X, there exists a net (Sα) of finite-rank operators from Z to X with ‖Sα‖≤λT such that lim α‖Sαz−Tz‖=0 for every z∈Z.
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