Weakly sequentially continuous differentiable mappings
The authors consider differentiable mappings \(f:U\subset X \rightarrow Y\), where \(X\) and \(Y\) are real Banach spaces and \(U\) is an open convex subset of \(X\). They characterize the mappings \(f\) which are weakly sequentially continuous in terms of the properties of the derivative \(f':U\subset X \rightarrow \mathcal{L}(X,Y)\). As a consequence, among other results, they obtain differentiable characterizations for the spaces containing no copies of \(\ell_1\) and for the spaces containing \(\ell_1\) and failing the Schur property.
Banach space not containing \(\ell _{1}\)
scientific article; zbMATH DE number 5626936
scientific article