β Scribed by Gilles Godefroy; Mohammed Yahdi; Robert Kaufman
No coin nor oath required. For personal study only.
Let X be a non-re exive Banach space such that X * is separable. Let N(X ) be the set of all equivalent norms on X , equipped with the topology of uniform convergence on bounded subsets of X . We show that the subset Z of N(X ) consisting of FrΓ echet-di erentiable norms whose dual norm is not strictly convex reduces any di erence of analytic sets. It follows that Z is exactly a di erence of analytic sets when N(X ) is equipped with the standard E ros-Borel structure. Our main lemma elucidates the topological structure of the norm-attaining linear forms when the norm of X is locally uniformly rotund.
π SIMILAR VOLUMES
Let E be a separable Banach space with separable dual. We show that the operation of subdi erentiation and the inverse operation are Borel from the convex functions on E into the monotone operators on E (subspace of the closed sets of E Γ E \* ) for the E ros-Borel structures. We also prove that th
We extend the Trotter-Kato-Chernoff theory of strong approximation of C 0 semigroups on Banach spaces to operator-norm approximation of analytic semigroups with error estimate. As application we obtain a criterion for the operator-norm convergence of the Trotter product formula on Banach spaces with