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arXiv · 0901.1512

Isometries on extremely non-complex Banach spaces

Piotr Koszmider·Miguel Martin·Javier Meri
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Abstract

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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Piotr Koszmider, Miguel Martin, Javier Meri. 2009-01-12. Isometries on extremely non-complex Banach spaces. https://arxiv.org/abs/0901.1512

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