Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On noncommutative weighted local ergodic theorems   In the present paper we consider a von Neumann algebra M with a faithful
normal semi-finite trace $\t$, and $\{\alpha_ t\} $ a strongly continuous
extension to $L^p(M,\t)$ of a semigroup of absolute contractions on $L^1
(M,\tau)$. By means of a non-commutative Banach Principle we prove for a
Besicovitch function b and $x\in L^p(M,\t)$, the averages
\frac{1}{T}\int_0^Tb(t)\a_t(x)dt converge bilateral almost uniform in
$L^p(M,\t)$ as $T\to 0$.

23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin