Theory of Fréchet cones
Concerning a geometrical characterization of Fréchet differentiability
On coincidence of Pettis and McShane integrability
R. Deville and J. Rodríguez proved that, for every Hilbert generated space , every Pettis integrable function is McShane integrable. R. Avilés, G. Plebanek, and J. Rodríguez constructed a weakly compactly generated Banach space and a scalarly null (hence Pettis integrable) function from into , which was not McShane integrable. We study here the mechanism behind the McShane integrability of scalarly negligible functions from (mostly) into spaces. We focus in more detail on the behavior...
On singlevaluedness and (strong) upper semicontinuity of maximal monotone mappings
Concerning interior mapping theorem
Once more on continuity of maximal monotone mappings
Sub differentiability and trustworthiness in the light of a new variational principle of Borwein and Preiss
Foreword
A generalization of the interior mapping theorem of Clarke and Pourciau
On uniformly Gâteaux smooth -smooth norms on separable Banach spaces
Every separable Banach space with -smooth norm (Lipschitz bump function) admits an equivalent norm (a Lipschitz bump function) which is both uniformly Gâteaux smooth and -smooth. If a Banach space admits a uniformly Gâteaux smooth bump function, then it admits an equivalent uniformly Gâteaux smooth norm.
Remarks on continuous images of Radon-Nikodým compacta
A family of compact spaces containing continuous images of Radon-Nikod’ym compacta is introduced and studied. A family of Banach spaces containing subspaces of Asplund generated (i.e., GSG) spaces is introduced and studied. Further, for a continuous image of a Radon-Nikod’ym compact we prove: If is totally disconnected, then it is Radon-Nikod’ym compact. If is adequate, then it is even Eberlein compact.
A note on lattice renormings
It is shown that every strongly lattice norm on can be approximated by smooth norms. We also show that there is no lattice and Gâteaux differentiable norm on .
Foreword
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