Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vector lattices admitting a positively homogeneous continuous function
  calculus   We characterize the Archimedean vector lattices that admit a positively
homogeneous continuous function calculus by showing that the following two
conditions are equivalent for each $n$-tuple $\boldsymbol{x} =
(x_1,\ldots,x_n)\in X^n$, where $X$ is an Archimedean vector lattice and
$n\in\mathbb N$:
  - there is a vector lattice homomorphism $\Phi_{\boldsymbol{x}}\colon H_n\to
X$ such that $\Phi_{\boldsymbol{x}}(\pi_i^{(n)})=x_i$ $(i\in\{1,\ldots,n\})$,
where $H_n$ denotes the vector lattice of positively homogeneous, continuous,
real-valued functions defined on $\mathbb R^n$ and $\pi_i^{(n)}\colon\mathbb
R^n\to\mathbb R$ is the $i^{\text{th}}$ coordinate projection;
  - there is a positive element $e\in X$ such that $e\geqslant\lvert
x_1\rvert\vee\cdots\vee\lvert x_n\rvert$ and the norm $\lVert x\rVert_e =
\inf\bigl\{\lambda\in[0,\infty)\:\colon\:\lvert x\rvert\le\lambda e\bigr\}$,
defined for each $x$ in the order ideal $I_e$ of $X$ generated by $e$, is
complete when restricted to the closed sublattice of $I_e$ generated by
$x_1,\ldots,x_n$.
  Moreover, we show that a vector space which admits a `sufficiently strong'
$H_n$-function calculus for each $n\in\mathbb N$ is automatically a vector
lattice, and we explore the situation in the non-Archimedean case by showing
that some non-Archimedean vector lattices admit a positively homogeneous
continuous function calculus, while others do not.

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The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph