Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterisation of Ces\`aro and $L$-Asymptotic Limits of Matrices   The main goal of this paper is to characterise all the possible Ces\`aro and
$L$-asymptotic limits of powerbounded, complex matrices. The investigation of
the $L$-asymptotic limit of a powerbounded operator goes back to Sz.-Nagy and
it shows how the orbit of a vector behaves with respect to the powers. It turns
out that the two types of asymptotic limits coincide for every powerbounded
matrix and a special case is connected to the description of the products
$SS^*$ where $S$ runs through those invertible matrices which have unit
columnvectors. We also show that for any powerbounded operator acting on an
arbitrary complex Hilbert space the norm of the $L$-asymptotic limit is greater
than or equal to 1, unless it is zero; moreover, the same is true for the
Ces\`aro asymptotic limit of a not necessarily powerbounded operator, if it
exists.

11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn