Isometries on extremely non-complex Banach spaces

Details Isometries on extremely non-complex Banach spaces Isometries on extremely non-complex Banach spaces

2009-01-12

arxiv.org/abs/0901.1512v2

Mathematics

Functional Analysis

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

Scientific paper

Given a separable Banach space $E$, we construct an extremely non-complex Banach space (i.e. a space satisfying that $\|Id + T^2\|=1+\|T^2\|$ 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 $\pm Id$, but the group of surjective isometries of its dual contains the group of isometries of a separable infinite-dimensional Hilbert space as a subgroup.

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