Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The operator system of Toeplitz matrices   A recent paper of A.~Connes and W.D.~van Suijlekom identifies the operator
system of $n\times n$ Toeplitz matrices with the dual of the space of all
trigonometric polynomials of degree less than $n$. The present paper examines
this identification in somewhat more detail by showing explicitly that the
Connes--van Suijlekom isomorphism is a unital complete order isomorphism of
operator systems. Consequences of this complete order isomorphism are also
examined, yielding two special results of note: (i) that every positive linear
map of the $n\times n$ complex matrices is completely positive when restricted
to the operator subsystem of Toeplitz matrices and (ii) that every linear
unital isometry of the $n\times n$ Toeplitz matrices into the algebra of all
$n\times n$ complex matrices is a unitary similarity transformation. This
latter result gives a new proof of a theorem established earlier.
  An operator systems approach to Toeplitz matrices yields new insights into
the positivity of block Toeplitz matrices, which are viewed herein as elements
of tensor product spaces of an arbitrary operator system with the operator
system of $n\times n$ complex Toeplitz matrices. In particular, it is shown
that min and max positivity are distinct if the blocks themselves are Toeplitz
matrices, and that the maximally entangled Toeplitz matrix generates an
extremal ray in the cone of all continuous $n\times n$ Toeplitz-matrix valued
functions $f$ on the unit circle $S^1$ whose Fourier coffecients $\hat f(k)$
vanish for $|k|\geq n$ .

19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th