Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral-free methods in the theory of hereditarily indecomposable
  Banach spaces   We give new and simple proofs of some classical properties of hereditarily
indecomposable Banach spaces, including the result by W. T. Gowers and B.
Maurey that a hereditarily indecomposable Banach space cannot be isomorphic to
a proper subspace of itself. These proofs do not make use of spectral theory
and therefore, they work in real spaces as well as in complex spaces. We use
our method to prove some new results. For example, we give a quantitative
version of the latter result by Gowers and Maurey and deduce that Banach spaces
that are isometric to all of their subspaces should have an unconditional basis
with unconditional constant arbitrarily close to $1$. We also study the
homotopy relation between into isomorphisms in hereditarily indecomposable
spaces.

8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin