Subspaces of almost Daugavet spaces

Lücking, Simon

doi:10.1090/S0002-9939-2010-10722-0

Subspaces of almost Daugavet spaces
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by Simon Lücking PDF

Proc. Amer. Math. Soc. 139 (2011), 2777-2782 Request permission

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 $Z$ is a closed subspace of a separable almost Daugavet space $X$ such that the quotient space $X/Z$ contains no copy of $\ell _1$, then $Z$ has the almost Daugavet property too.

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