The Fitzpatrick function and nonreflexive spaces

Banach Spaces of Type (NI) and Monotone Operators on Non-reflexive Spaces

A convex set C ⊆ X∗∗ × X∗ admits the variant Banach-Dieudonné property (VBDP) if the weak∗-strong closure C w×‖·‖ is the smallest set containing C that is closed to all limits of its bounded and weak∗×‖ · ‖ convergent nets. We show in particular, that all convex sets in X∗∗×X∗ admit the VBDP when E∗ := X∗×X∗∗ is weakly-compactly generated (WCG) and hence if E is either a dual separable or a ref...

A proximal point method in nonreflexive Banach spaces

We propose an inexact version of the proximal point method and study its properties in nonreflexive Banach spaces which are duals of separable Banach spaces, both for the problem of minimizing convex functions and of finding zeroes of maximal monotone operators. By using surjectivity results for enlargements of maximal monotone operators, we prove existence of the iterates in both cases. Then w...

Majorization in de Branges spaces II. Banach spaces generated by majorants

This is the second part in a series dealing with subspaces of de Branges spaces of entire function generated by majorization on subsets of the closed upper half-plane. In this part we investigate certain Banach spaces generated by admissible majorants. We study their interplay with the original de Branges space structure, and their geometry. In particular, we will show that, generically, they w...

Extensions of an Ac(σ) Functional Calculus

On a reflexive Banach space X , if an operator T admits a functional calculus for the absolutely continuous functions on its spectrum σ(T ) ⊆ R, then this functional calculus can always be extended to include all the functions of bounded variation. This need no longer be true on nonreflexive spaces. In this paper, it is shown that on most classical separable nonreflexive spaces, one can constru...

Nonlinear fractional differential equations in nonreflexive Banach spaces and fractional calculus