Extremely strict ideals in Banach spaces

Abstract

Motivated by the notion of an ideal introduced by Godefroy et al. (Studia Math. 104 (1993) 13–59), in this article, we introduce and study the notion of an extremely strict ideal. For a Poulsen simplex K, we show that the space of affine continuous functions on K is an extremely strict ideal in in the space of continuous functions on K. For injective tensor product spaces, we prove a cancelation theorem for extremely strict ideals. We also exhibit non-reflexive Banach spaces which are not strict ideals in their fourth dual.