Order-isomorphism and a projection's diagram of C(X)

Ahmed S. Al-Rawashdeh, Sultan M. Al-Suleiman

Research output: Contribution to journalArticlepeer-review

Abstract

A mapping between projections of C* -algebras preserving the orthogonality, is called an orthoisomorphism. We define the order-isomorphism mapping on C* -algebras, and using Dye's result, we prove in the case of commutative unital C* -algebras that the concepts; order-isomorphism and the orthoisomorphism coincide. Also, we define the equipotence relation on the projections of C(X); indeed, new concepts of finiteness are introduced. The classes of projections are represented by constructing a special diagram, we study the relation between the diagram and the topological space X. We prove that an order-isomorphism, which preserves the equipotence of projections, induces a diagram-isomorphism; also if two diagrams are isomorphic, then the C* -algebras are isomorphic.

Original languageEnglish
Pages (from-to)523-536
Number of pages14
JournalTurkish Journal of Mathematics
Volume34
Issue number4
DOIs
Publication statusPublished - 2010

Keywords

  • Clopen subsets
  • Commutative C* -algebras
  • Infinite projections
  • Projections order-isomorphism

ASJC Scopus subject areas

  • General Mathematics

Fingerprint

Dive into the research topics of 'Order-isomorphism and a projection's diagram of C(X)'. Together they form a unique fingerprint.

Cite this