ProV Logo
0
Domains of commutative C*-subalgebras
Heunen, Chris...

Free

Domains of commutative C*-subalgebras by Heunen, Chris ( Author )
Lemonjar Open Access
N.A
10-04-2015
A C*-algebra is determined to a great extent by the partial order of its commutative C*-algebras. We study order-theoretic properties of this dcpo. Many properties coincide: the dcpo is, equivalently, algebraic, continuous, meet-continuous, atomistic, quasi-algebraic, or quasi-continuous, if and only if the C*-algebra is scattered. For C*-algebras with enough projections, these properties are equivalent to finite-dimensionality. Approximately finite-dimensional elements of the dcpo correspond to Boolean subalgebras of the projections of the C*-algebra, which determine the projections up to isomorphism. Scattered C*-algebras are finite-dimensional if and only if their dcpo is Lawson-scattered. General C*-algebras are finite-dimensional if and only if their dcpo is order-scattered.
-
Article
pdf
36.88 KB
English
-
MYR 0.00
-
https://arxiv.org/abs/1504.02730
Share this eBook