The Dual Form of the Approximation Property for a Banach Space and a Subspace
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چکیده
Given a Banach space X and a subspace Y , the pair (X,Y ) is said to have the approximation property (AP) provided there is a net of finite rank bounded linear operators on X all of which leave the subspace Y invariant such that the net converges uniformly on compact subsets of X to the identity operator. The main result is an easy to apply dual formulation of this property. Applications are given to three space properties; in particular, if X has the approximation property and its subspace Y is L∞, then X/Y has the approximation property. In memory of A. Pe lczyński
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تاریخ انتشار 2015