Cp-classes of operators in C-algebras

Cp-classes of operators in C-algebras

We construct a suitable representation of a C*-algebra that carries single elements to rank one operators. We also prove an abstract spectral theorem for compact elements in the algebra. This leads naturally to an abstract definition of Cp-classes of compact elements in the algebra.

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Veröffentlicht in:Journal of the Australian Mathematical Society (2001) 1986-04, Vol.40 (2), p.153-160
1. Verfasser: Giotopoulos, S.
Format: Artikel
Sprache:eng
Schlagworte:
46 L 05
47 B 10
C-algebra
Cp-classes of operators
minimal deal
representation
spectral theorem
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Zusammenfassung:We construct a suitable representation of a C*-algebra that carries single elements to rank one operators. We also prove an abstract spectral theorem for compact elements in the algebra. This leads naturally to an abstract definition of Cp-classes of compact elements in the algebra.
ISSN:0263-6115
1446-7887
1446-8107
DOI:10.1017/S1446788700027142