Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Crossed-Product Extensions of $L_p$-Bounds for Amenable Actions   We will extend earlier transference results of Neuwirth and Ricard from the
context of noncommutative $L_p$-spaces associated with amenable groups to that
of noncommutative $L_p$-spaces over crossed products of amenable and
trace-preserving actions. Namely, if $T_m:L_p(\mathcal{L} G) \rightarrow
L_p(\mathcal{L} G)$ is a completely bounded Fourier multiplier, where
$\mathcal{L} G \subset \mathcal{B}(L_2 G)$ is the von Neumann algebra of $G$,
we will see that $\mathrm{Id} \rtimes T_m: L_p(\mathcal{M} \rtimes_\theta G)
\rightarrow L_p(\mathcal{M} \rtimes_\theta G)$ is also completely bounded and
that $$
  \| \mathrm{Id} \rtimes T_m: L_p(\mathcal{M} \rtimes_\theta G) \rightarrow
L_p(\mathcal{M} \rtimes_\theta G) \|_{\mathrm{cb}} \leq \| T_m \|_{\mathrm{cb}}
$$ provided that $\theta$ is amenable and trace-preserving. Furthermore, our
construction allow to extend $G$-equivariant completely bounded operators $S:
L_p(\mathcal{M}) \rightarrow L_p(\mathcal{M})$ to the crossed-product, so that
$$
  \|S \rtimes \mathrm{Id}: L_p(\mathcal{M} \rtimes_\theta G) \rightarrow
L_p(\mathcal{M} \rtimes_\theta G) \|_{\mathrm{cb}} \leq C^\frac{1}{p} \, \| S
\|_{\mathrm{cb}} $$ whenever $\theta$ is trace-preserving, amenable and its
generalized F{\o}lner sets satisfy certain accretivity property measured by the
constant $1 \leq C$. As a corollary, we will obtain stability results for
maximal $L_p$-bounds over crossed products. Such results imply the stability of
certain assumptions recently used to prove a noncommutative generalization of
the spectral H\"omander-Mikhlin theorem.

1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat