Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maps preserving peripheral spectrum of generalized Jordan products of
  operators   Let $X_1$ and $X_2$ be complex Banach spaces with dimension at least three,
$\mathcal{A}_1$ and $\mathcal{A}_2$ be standard operator algebras on $X_1$ and
$X_2$, respectively. For $k\geq2$, let $(i_1,...,i_m)$ be a sequence with terms
chosen from $\{1,\ldots,k\}$ and assume that at least one of the terms in
$(i_1,\ldots,i_m)$ appears exactly once. Define the generalized Jordan product
$T_1\circ T_2\circ\cdots\circ T_k=T_{i_1} T_{i_2}\cdots T_{i_m}+T_{i_m}\cdots
T_{i_2} T_{i_1}$ on elements in $\mathcal{A}_i$. This includes the usual Jordan
product $A_1A_2+A_2A_1$, and the Jordan triple $A_1A_2A_3+A_3A_2A_1$. Let
$\Phi:\mathcal{A}_1\rightarrow\mathcal{A}_2$ be a map with range containing all
operators of rank at most three. It is shown that $\Phi$ satisfies that
$\sigma_\pi(\Phi(A_1)\circ\cdots\circ\Phi(A_k))=\sigma_\pi(A_1\circ\cdots\circ
A_k)$ for all $A_1, \ldots, A_k$, where $\sigma_\pi(A)$ stands for the
peripheral spectrum of $A$, if and only if $\Phi$ is a Jordan isomorphism
multiplied by an $m$th root of unity.

18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th