Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representations of $*$-semigroups associated to invariant kernels with
  values adjointable operators. I   We consider positive semidefinite kernels valued in the $*$-algebra of
adjointable operators on a VE-space (Vector Euclidean space) and that are
invariant under actions of $*$-semigroups. A rather general dilation theorem is
stated and proved: for these kind of kernels, representations of the
$*$-semigroup on either the VE-spaces of linearisation of the kernels or on
their reproducing kernel VE-spaces are obtainable. We point out the reproducing
kernel fabric of dilation theory and we show that the general theorem unifies
many dilation results at the non topological level.

26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph