Isometries on extremely non-complex Banach spaces

2009/01/12 by Piotr Koszmider, Koszmider, Piotr, Miguel Martin +5
Mathematics · #Advanced Banach Space Theory #Advanced Topics in Algebra #Holomorphic and Operator Theory #math.FA #math.OA #msc:46B04 #msc:46B10 #msc:46B20 #msc:46E15 #msc:47A99

paper · pdf · doi:10.48550/arxiv.0901.1512

18 pages, revised version, to appear in J. Inst. Math. Jussieu

arxiv created 2010/01/29 · arxiv updated 2010/02/08

Abstract

Given a separable Banach space E, we construct an extremely non-complex Banach space (i.e. a space satisfying that ‖Id + T²‖=1+‖T²‖ for every bounded linear operator T on it) whose dual contains E^* as an L-summand. We also study surjective isometries on extremely non-complex Banach spaces and construct an example of a real Banach space whose group of surjective isometries reduces to ± 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.

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