Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On functional calculus for Hermitian elements of Banach algebras: the
  norm and spectral radius   Let $ A$ be a complex unital Banach algebra. An element $a \in A$ is said to
be Hermitian, if $ \| \exp (ita) \| =1$ for all $t\in R$. In the case of the
algebra of bounded linear operators in a Hilbert space this Hermitian property
agrees with the ordinary selfadjointness. If $a \in A$ is Hermitian, then
$|a|=||a||$, where $|a|$ denotes the spectral radius of $a$. A function $F:
R\to \C$ is called the universal symbol if $ \|| F(a)||= |F(a)|$\ for each $ A$
and all Hermitian $a\in A$. We characterize universal symbols in terms of
positive definite functions.

15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess