On bases, finite dimensional decompositions and weaker structures in Banach spaces
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This is an investigation of the connections between bases and weaker structures in Banach spaces and their duals. It is proved, e.g., thatX has a basis ifX* does, and that ifX has a basis, thenX* has a basis provided thatX* is separable and satisfies Grothendieck’s approximation property; analogous results are obtained concerning π-structures and finite dimensional Schauder decompositions. The basic results are then applied to show that every separableℒ p space has a basis.
KeywordsBanach Space Approximation Property Natural Projection Separable Banach Space Invertible Operator
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