Abstract of a paper by Piotr Koszmider, Miguel Martin and Javier Meri
This is an announcement for the paper "Isometries on extremely non-complex Banach spaces" by Piotr Koszmider, Miguel Martin and Javier Meri . Abstract: We construct an example of a real Banach space whose group of surjective isometries reduces to $\pm\Id$, but the group of surjective isometries of its dual contains the group of isometries of a separable infinite-dimensional Hilbert space as a subgroup. To do so, we present examples of extremely non-complex Banach spaces (i.e.\ spaces $X$ such that $\|\Id + T^2\|=1+\|T^2\|$ for every bounded linear operator $T$ on $X$) which are not of the form $C(K)$, and we study the surjective isometries on this class of Banach spaces. Archive classification: math.FA math.OA Mathematics Subject Classification: Primary: 46B04. Secondary: 46B10, 46B20, 46E15, 47A99 Remarks: 20 pages The source file(s), KoszmiderMartinMeri.tex: 84147 bytes, is(are) stored in gzipped form as 0901.1512.gz with size 24kb. The corresponding postcript file has gzipped size 138kb. Submitted from: mmartins@ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0901.1512 or http://arXiv.org/abs/0901.1512 or by email in unzipped form by transmitting an empty message with subject line uget 0901.1512 or in gzipped form by using subject line get 0901.1512 to: math@arXiv.org.
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