Generic differentiability of mappings and convex functions in Banach and locally convex spaces
(I)-envelopes of unit balls and James' characterization of reflexivity
We study the (I)-envelopes of the unit balls of Banach spaces. We show, in particular, that any nonreflexive space can be renormed in such a way that the (I)-envelope of the unit ball is not the whole bidual unit ball. Further, we give a simpler proof of James' characterization of reflexivity in the nonseparable case. We also study the spaces in which the (I)-envelope of the unit ball adds nothing.
Induced ...-Homomorphisms and a Parametrization of Measurable Sections via Extremal Preimage Measures.
Integral Representation in the Set of Solutions of a Generalized Moment Problem.
Integral representations in conuclear cones.
Interdependence of some problems arising in generalizing the Marcus-de Oliveira determinantal conjecture
Inverse limits need not exist in the category of compact spaces and Feller kernels: a counterexample
Isometries and the Complex State Spaces of Uniform Algebras.
Korovkinhüllen in Funktionenräumen.
Large subsets of dual Banach spaces
Les points extremes et les points unis de la boule unitée étudiés au moyen du semi-produit scalaire
Limit semigroups of Bernstein-Schnabl operators associated with positive projections
Lipschitz extensions of convex-valued maps
Si dimostra che ogni funzione multivoca lipschitziana con costante di Lipschitz , definita su un sottoinsieme di uno spazio di Hilbert a valori compatti e convessi in , può essere estesa su tutto ad una funzione multivoca lipschitziana con costante minore di 7 nM. In generale, non esistono invece estensioni aventi la stessa costante di Lipschitz .
Local completeness of locally pseudoconvex spaces and Borwein-Preiss variational principle
The notion of local completeness is extended to locally pseudoconvex spaces. Then a general version of the Borwein-Preiss variational principle in locally complete locally pseudoconvex spaces is given, where the perturbation is an infinite sum involving differentiable real-valued functions and subadditive functionals. From this, some particular versions of the Borwein-Preiss variational principle are derived. In particular, a version with respect to the Minkowski gauge of a bounded closed convex...
Mesures coniques et intégrale de Daniell
Metrization of Compact Convex Sets.
Minimal pairs of bounded closed convex sets as minimal representations of elements of the Minkowski-Rådström-Hörmander spaces
The theory of minimal pairs of bounded closed convex sets was treated extensively in the book authored by D. Pallaschke and R. Urbański, Pairs of Compact Convex Sets, Fractional Arithmetic with Convex Sets. In the present paper we summarize the known results, generalize some of them and add new ones.
Minimal pairs of compact convex sets
Pairs of compact convex sets naturally arise in quasidifferential calculus as sub- and superdifferentials of a quasidifferentiable function (see Dem86). Since the sub- and superdifferentials are not uniquely determined, minimal representations are of special importance. In this paper we give a survey on some recent results on minimal pairs of closed bounded convex sets in a topological vector space (see PALURB). Particular attention is paid to the problem of characterizing minimal representatives...
Monotone extenders for bounded c-valued functions
Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, the set of all bounded continuous functions f: A → c, and the set of all functions f: X → c which are continuous at each point of A ⊂ X. We show that a Tikhonov subspace A of a topological space X is strong Choquet in X if there exists a monotone extender . This shows that the monotone extension property for bounded c-valued functions can fail in GO-spaces, which provides a negative answer to a question...
Note on separation of convex sets