Quotients of Banach spaces with the Daugavet property

Details Quotients of Banach spaces with the Daugavet property Quotients of Banach spaces with the Daugavet property

2008-06-11

arxiv.org/abs/0806.1815v1

Bull. Pol. Acad. Sci. 56, no.2, 131-147 (2008)

Mathematics

Functional Analysis

15 pages

Scientific paper

We consider a general concept of Daugavet property with respect to a norming subspace. This concept covers both the usual Daugavet property and its weak$^*$ analogue. We introduce and study analogues for narrow operators and rich subspaces in this general setting and apply the results to show that a quotient of $L_1[0,1]$ over an $\ell_1$-subspace can fail the Daugavet property. The latter answers a question posed to us by A. Pelczynski in the negative.

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