An extension of James's compactness theorem
Abstract
Let X and Y be Banach spaces and F a subset of BY*. Endow Y with the topology τF of pointwise convergence on F. Let T: X* Y be a bounded linear operator which is (w*, τF) continuous. Assume that every vector in the range of T attains its norm at an element of F. Then it is proved that T is (w*,w) continuous.
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