[Banach] Abstract of a paper by Vladimir Kadets, Varvara Shepelska and Dirk Werner

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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