A Stone–Weierstrass theorem for Banach function spaces satisfying a certain separation property

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

A nonconvex separation property in Banach spaces

We establish, in innnite dimensional Banach space, a nonconvex separation property for general closed sets that is an extension of Hahn-Banach separation theorem. We provide some consequences in optimization, in particular the existence of singular multipliers and show the relation of our principle with the extremal principle of Mordukhovich.

a mean ergodic theorem for asymptotically quasi-nonexpansive affine mappings in banach spaces satisfying opial's condition

The Reconstruction Property in Banach Spaces and a Perturbation Theorem

Perturbation theory is a fundamental tool in Banach space theory. However, the applications of the classical results are limited by the fact that they force the perturbed sequence to be equivalent to the given sequence. We will develop a more general perturbation theory that does not force equivalence of the sequences.

a mean ergodic theorem for asymptotically quasi-nonexpansive affine mappings in banach spaces satisfying opial's condition

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