Semi denting points and related notions in Banach spaces

Abstract

In this work, we study semi denting points and related notions in Banach spaces. We observe that $X$ has the Radon-Nikodým Property if and only if every closed bounded convex set has a semi denting point. We also study the stability properties of semi denting, semi PC, and semi SCS points, as well as their $w^{\ast }$-analogues in Banach spaces, with respect to $l_p$-sums ( $1\le p\le \infty$), ideals, and projective tensor products.

arXiv comment21 pages