Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Direct integrals of matrices   It is shown that each linear operator on a separable Hilbert space which
generates a finite type I von Neumann algebra has, up to unitary equivalence, a
unique representation as a direct integral of inflations of mutually unitary
inequivalent irreducible matrices. This leads to a simplification of the
so-called prime (or central) decomposition and the multiplicity theory for such
operators. The concept of so-called p-isomorphisms between special classes of
such operators is discussed. All results are formulated in more general
settings; that is, for tuples of closed densely defined operators affiliated
with finite type I von Neumann algebras.

17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys