This is an announcement for the paper "Quotients of Banach spaces with the Daugavet property" by Vladimir Kadets, Varvara Shepelska and Dirk Werner.

Abstract: 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.

Archive classification: math.FA

Mathematics Subject Classification: 46B04; 46B25; 47B38

Remarks: 15 pages

The source file(s), dpry_bullpol_june08.tex: 55217 bytes, is(are) stored in gzipped form as 0806.1815.gz with size 17kb. The corresponding postcript file has gzipped size 114kb.

Submitted from: werner@math.fu-berlin.de

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