Subspaces of almost Daugavet spaces

Abstract

We study the almost Daugavet property, a generalization of the Daugavet property. We analyze what kind of subspaces and sums of Banach spaces with the almost Daugavet property have this property as well. The main result of the paper is that if Z Z is a closed subspace of a separable almost Daugavet space X X such that the quotient space X / Z X/Z contains no copy of ℓ 1 \ell _1 , then Z Z has the almost Daugavet property too.