Isometries on Extremely Non-complex Banach Spaces
نویسنده
چکیده
We 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. To do so, we present examples of extremely non-complex Banach spaces (i.e. spaces X such that ‖ Id+T ‖ = 1+‖T ‖ 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.
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