An extension of James's compactness theorem
Functional Analysis
2014-07-15 v1
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.
Cite
@article{arxiv.1407.3655,
title = {An extension of James's compactness theorem},
author = {Ioannis Gasparis},
journal= {arXiv preprint arXiv:1407.3655},
year = {2014}
}
Comments
15 pages