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Cp-classes of operators in C*-algebras

Part of: Selfadjoint operator algebras Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

S. Giotopoulos
S. Giotopoulos
Affiliation:
Section of Mathematical Analysis and its Application, Department of Mathematics, University of Athens, Panepistemiopolis, 157 81 Athens, Greece
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Abstract

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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.

Keywords

C*-algebraminimal dealrepresentationspectral theoremCp-classes of operators

MSC classification

Secondary: 46L05: General theory of $C^*$-algebras 47B10: Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 40 , Issue 2 , April 1986 , pp. 153 - 160
Copyright
Copyright Australian Mathematical Society 1986

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