On Paving Sequences in C ∗ -Algebras

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1990Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 110, page 159 (issn: 0002-9939,

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Authors: Kaplan, Alexander;

doi: 10.2307/2048255

On Paving Sequences in C ∗ -Algebras

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Abstract

The author introduces the notion of a paving sequence in a \(C^*\)- algebra. A UHF algebra has such a sequence. It is shown that a \(C^*\)- algebra with a paving sequence is simple and in the unital case it is nuclear. It is also shown that under certain conditions, a correspondence between paving sequences of two \(C^*\)-algebras induces a *-homomorphism between them.

Keywords

Haagerup dual, General theory of \(C^*\)-algebras, simple paving structure, tower, paving sequence in a \(C^ *\)-algebra, *-homomorphism, UHF algebra

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