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banach spaces of continuous functions

Journal of the Institute of Mathematics of Jussieu (1)

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1 results

Isometries on extremely non-complex Banach spaces
Part of
- Normed linear spaces and Banach spaces; Banach lattices
Piotr Koszmider, Miguel Martín, Javier Merí
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 10 / Issue 2 / April 2011

Published online by Cambridge University Press:

14 July 2010, pp. 325-348

Print publication:

April 2011
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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.