Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isometries on extremely non-complex Banach spaces   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.

28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
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The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex