270 research outputs found
An extension of James's compactness theorem
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.Comment: 15 page
On the complemented subspaces of the Schreier spaces
It is shown that the Schreier space X admits a set of continuum cardinality
whose elements are mutually incomparable complemented subspaces spanned by
subsequences of the natural Schauder basis of X.Comment: 26 pages, AMS-LaTe
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