Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the structure of semigroups on $L_p$ with a bounded
  $H{^\infty}$-calculus   We show that a bounded analytic semigroup on an $L_p$-space has a bounded
$H^{\infty}(\Sigma_{\varphi})$-calculus for some $\varphi < \frac{\pi}{2}$ if
and only if the semigroup can be obtained, after restricting to invariant
subspaces, factorizing through invariant subspaces and similarity transforms,
from a bounded analytic semigroup on some bigger $L_p$-space which is positive
and contractive on the real line.

15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg