[Banach] 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.