A Remark on Strongly Exposing Functionals

On Strongly Exposing Functionals

Let X be a real Banach space and let K be a bounded closed convex subset of X. We prove that the set of strongly exposing functions K" of K is a (norm) dense G, in X* if and only if for any bounded closed convex subset C such that Kit C, there exists a point x in K which is a strongly exposed point of conv (C U K). As an application, we show that if X* is weakly compact generated, then for any ...

A remark on multiobjective stochastic optimization via strongly convex functions

Many economic and financial applications lead (from the mathematical point of view) to deterministic optimization problems depending on a probability measure. These problems can be static (one stage), dynamic with finite (multistage) or infinite horizon, single objective or multiobjective.We focus on one-stage case in multiobjective setting. Evidently, well known results from the deterministic ...

A Remark on Continuity of Positive Linear Functionals on Separable Banach *-Algebras

Using a variation of the Murphy-Varopoulos Theorem, we give a new proof of the following R. J. Loy Theorem: Let A be a separable Banach ∗-algebra with center Z such that ZA has at most countable codimension, then every positive linear functional on A is continuous.

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Remark on a Reply

1.1 In their original PNAS article Macy and Sato (2002) make it clear that their main point concerns social mobility (see, for instance, the abstract and the last section). Their central claim is the non-monotonic effect of mobility: with moderate mobility, they maintain, trust can be established; with too much mobility, trust and trustworthiness are undermined — and therefore their "warning fl...