Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On C*-Extreme Maps and *-Homomorphisms of a Commutative C*-Algebra   The generalized state space of a commutative C*-algebra, denoted S_H(C(X)),
is the set of positive unital maps from C(X) to the algebra B(H) of bounded
linear operators on a Hilbert space H. C*-convexity is one of several
non-commutative analogs of convexity which have been discussed in this context.
In this paper we show that a C*-extreme point of S_H(C(X)) satisfies a certain
spectral condition on the operators in the range of the associated positive
operator-valued measure. This result enables us to show that C*-extreme maps
from C(X) into K^+, the algebra generated by the compact and scalar operators,
are multiplicative. This generalizes a result of D. Farenick and P. Morenz. We
then determine the structure of these maps.

4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex