This is an announcement for the paper "An extension of James's compactness theorem" by Ioannis Gasparis.

Abstract: Let X and Y be Banach spaces and F a subset of B_{Y^*}. Endow Y with the topology \tau_F of pointwise convergence on F. Let T: X^* \to Y be a bounded linear operator which is (w^*, \tau_F) 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.

Archive classification: math.FA

Mathematics Subject Classification: 46

Remarks: 15 pages

Submitted from: ioagaspa@math.ntua.gr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1407.3655

or

http://arXiv.org/abs/1407.3655