Domains of commutative C*-subalgebras

Christiaan Heunen, Bert Lindenhovius

Research output: Contribution to journalArticlepeer-review

Abstract

A C*-algebra is determined to a great extent by the partial order of its commutative C*-subalgebras. 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. 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.
Original languageEnglish
Pages (from-to)972-1006
Number of pages41
JournalMathematical Structures in Computer Science
Volume29
Issue number7
Early online date21 Mar 2019
DOIs
Publication statusPublished - Aug 2019

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