Subspaces of almost Daugavet spaces

Details Subspaces of almost Daugavet spaces Subspaces of almost Daugavet spaces

2010-07-17

arxiv.org/abs/1007.2916v1

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

Mathematics

Functional Analysis

5 pages

Scientific paper

We study the almost Daugavet property, a generalization of the Daugavet property. It is analysed 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: 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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